Let’s take a quick walk down memory lane—to algebra class. Do you remember learning about exponential growth? You have an equation to work out, and then you map a curved line on some graph paper. It starts out low and gradual, but when it finally takes off, it skyrockets! 

If this sounds like Charlie What is compounding growth of an investment savings account teacher right now (wa-waa-waa-waaa), hang with us. Exponential growth explains how compound interest works, and—if you use it right—this powerful formula could make you millions of dollars.

So, let’s jump right in: What is compound interest and how does it work?  

What Is Compound Interest?

Compound interest is earning interest on top of interest. When old school runescape thieving money making invest money, you’re expecting to get a return on your money, meaning that you should end up with more money than you originally put in. If you leave that money alone (the initial principal plus the interest), compound interest applies the interest rate to the total new amount of money earned, so that it builds exponentially over time.  

Simple interest, on the other hand, does not accrue (fancy investing talk for build up over time). Once you pay (or earn) interest for a particular period, it’s gone. It’s not added to the next payment period the way compound interest is. 

Compound interest is the secret sauce for building wealth, and it’s one of the most basic principles of investing. If you want to build wealth, you have to get out of debt (paying interest) and start investing (earning interest).

How Does Compound Interest Work?

Compound interest is like a snowball that’s rolling downhill. As it picks up momentum over time, it gets bigger and bigger. Here’s an example:

Let’s say you invest $1, and—just to keep it simple—it earns 10% a year in interest. After one year, you’d have $1,—the original money plus $ interest that you earned. The second year, you’d have slightly more—$1,—because you’re earning interest on top of interest. The investment compounds, or builds up, what is compounding growth of an investment savings account, over time. Now $1, doesn’t seem like a big deal at first, but it becomes a big deal later. If we leave that $1, alone for 40 years, and it compounds annually at 10%, it will grow to a sum of over $53,! And all you put in was $1,!

The number of compounding periods will determine how quickly your investment grows. Interest can be compounded daily, what is compounding growth of an investment savings account, weekly or yearly.

Compound Annual Growth Rate (CAGR)

Compound Annual Growth Rate is an important investment concept that’s related to compound interest. It’s a way to measure the growth rate of your investments over time. When you’re investing to save for retirement, you should put your money in mutual funds. Mutual funds don’t earn a fixed interest rate. In fact, the value of a mutual fund can rise and fall. That’s why it’s important to choose mutual funds with a long history of strong returns.

When estimating the overall growth of mutual fund investments, some people use the long-term growth rate of the S&P The S&P is a common measuring stick for how the stock market is performing. 

The Power of Compounding

To help you see the power of compounding in action, here's the story of Jack and Blake—two guys who got serious about investing for retirement. They picked good, growth stock mutual funds that average an annual return of about %—just under the long-term growth rate of the S&P

Jack

• Starts investing at age 21
• Invests $2, every year
• Stops contributing money at age 30
• Total amount contributed: $21,

Blake

• Starts investing at age 30
• Invests $2, every year
• Contributes money until age 67 (a total of 37 years!)
• Total amount contributed: $91,

At age 67, Jack’s investment has grown to $2,, and Blake’s has grown to $1,! Nine years made a difference of over one million dollars.

So, while mutual fund investments don’t earn compound interest, they do experience compound growth—and as you can see, it works the same way! The secret sauce for harnessing the power of compound interest is time. The number of compounding periods is what makes your interest explode.

Compound Interest Formula

All right, math nerds, it’s your time to shine. Here’s how you calculate compound interest:

A = P(1+r/n)^nt

• P is the principal (starting amount)
• r is the interest rate
• n is the number of times the interest compounds each year
• t is the total number of years your money is invested
• A is your final amount

If you’re experiencing terrifying flashbacks to school days when you had to memorize math formulas for a test, don’t worry. We’ve got a compound interest calculator that will do the calculations for you.

How to Grow Your Investments With Compound Interest

The combination of compound interest (or growth) and time is the key to investing. But it won’t make you rich overnight. It’s all about having the right mindset. Stay focused for the long haul. Be disciplined. It will pay off in the end!

Remember: Interest that you pay is a penalty. Interest that you earn is a reward. Here are four key strategies to get your money working for you in compound interest:

1. Get out of debt.

Compound interest is a powerful force. You want it to work for you, not against you. If you’re in debt, you might be making compounding interest payments on a credit card. That’s why it feels like drowning—because the amount you owe keeps increasing. Avoid debt like the plague. Check out the debt snowball for a proven plan to destroy your debt—for good.

2. Start as soon as possible.

Remember Jack and Blake? The more compounding periods your money experiences, the larger it will grow. Start investing in growth stock mutual funds (either through your workplace retirement plan or a Roth IRA) as soon as you can.

3. Increase your contributions each year.

If you get a raise this year, earn some money through a side hustle, or come into some money through an inheritance, increase your contributions instead of increasing your standard of living. You should invest at least 15% of your income in retirement, and there are ways to invest more than 15% as your earnings increase. It will be worth it when you watch your investments explode.

4. Exercise patience.

Have a long-term mindset. The key to harnessing the power of compound interest is to leave your money alone for an extended amount of time. For the first few years, it might feel like nothing’s happening. But remember that exponential growth graph we talked about earlier? The longer you let it be, the higher it grows!  

It’s great to save money and build wealth, but what’s it all for? The whole point of understanding the power of compound interest is to be able to invest and reach your high definition retirement dreams. If you haven’t started planning for your financial future, reach out to an investing professional to help you get started. Our SmartVestor Program will connect you with qualified investing professionals in your area who can take a look at where you are and help you create a plan you can get started on.

Find a SmartVestor Pro in your area today!

It is rumored that Albert Einstein once quipped that the investir 100 em bitcoin powerful force in the universe is the principle of compounding. In investing and finance, this force manifests itself through the concept of compounding returns. In simple terms, compound interest means that you begin to earn interest on the interest you receive, which multiplies your money at an accelerated rate.

For example, if you have $ and earn 10% interest per year, you will have $ after one year. Then, if you earn 10% interest the next year on that $, you end up with $ by the end of year two. The process continues until, eventually, your original $ may be eclipsed by the amount of interest you gained.

This is one way many top investors find success in building their wealth. But it's not just for the top investors—you can take advantage of compound interest through savings accounts and investment portfolios. Learn how to do that below.

What Determines How Much Compound Interest You Can Earn?

There are three main factors that can influence the rate at which your money compounds:

1. The rate of return, or the profit, on your investment: For example, if you are investing in dividend-paying stocks, this would be your total profit from capital gains and dividends. If you were putting money in a savings account, this would be the annual percentage yield (APY).
2. Time:The more time you give your money to build upon itself, the more it compounds. For example, all things equal, your money would grow more over a year period than it would over a five-year period.
3. The tax rate, and when you have to pay taxes on your interest:You will end up with far more money if you don’t have to pay taxes at all, or at least not until the end of the compounding period rather than at the end of each year. This is why tax-deferred accounts, such as the traditional IRA, Roth IRA, (k), and SEP-IRA, are so important to consider.

Compound Interest and the Time Value of Money

The foundation behind compounding interest is the concept of the time value of money, which states that the value of money changes, depending upon when it is received. Having $ today is preferable to receiving it a few years from now because you can invest it to generate dividends and interest income. Compounding allows that money to grow. If you waited two years to receive that $, you'd miss out on two years of opportunity to earn compound interest. This is known as opportunity cost.

Opportunity cost is the loss of possible gains if an action is not chosen. In this case, the opportunity cost is equal to the amount of money you do not get in interest if you don't invest in that money.

In our earlier example, if you don't invest the $ in an account with 10% annual interest, what is compounding growth of an investment savings account lose the opportunity to earn $50 or more per year in interest. In 10 years, your $ could be $1, But if you don't invest it, it'll still be $ 10 years later.

When you understand the time value of money, you'll see that compounding and patience are the ingredients for building wealth.

Here's another example: Let's say you are 30 years old and want to have $1 million by the time you retire at age You can afford to save $ per month in an account with an 8% annual return on your investment. Will you be able to reach your goal? Using a compound interest calculator, you can see that you'd be able to turn that $ per month into $1 million after 29 years—six years earlier than you plan on retiring.

Compound Interest Results Over Time

Another way to understand the power of compound interest is to put values into a compound interest table that shows you just how much your wealth can multiply over time.

Imagine you're an investor who sets aside a lump sum of $10, Take a look at the table below to see the influence of time and different rates of return on this investment. Over time, saving money is not the only key to a large fortune; compound interest plays a big part.

For instance, a year-old who invests $10, today and parks it in Treasury bills, earning 4% per year, on average, for the next 50 years, will have $71, if the purchases were made through ​a tax-free account such as a Roth IRA. If they had invested in stocks and real estate, earning a 12% average annual rate of return over the same time, they would end up with $2, Adding asset classes with higher returns would result in over 40 times more money, thanks to the power of compounding.

How Compound Interest Could Impact Teens and Their Savings

Your teenage years are a good time what is compounding growth of an investment savings account start saving money for the future. Because you have time for that money to grow before you may need it to buy a house or retire, you can benefit greatly from compound interest. One easy way to start earning compound interest is to open a high-yield savings account and contribute a set amount to it every month. Over time. your money could grow a lot and allow you to build your wealth. While you may only be able to earn a small amount of interest in a savings account, the compound interest could add up over time. For example, if you contributed $50 per month to a high-yield savings account and earned % interest per year, you could have over $12, after 20 years.

Once you've got the savings part down, you could try your hand at investing to potentially benefit even more compound interest. For example, let's say you opened an investment account with the help of an adult (you usually need to be 18 years or older to invest). If you contributed $ per month to the investment account for 40 years, and earned a 10% annual rate of return on investment each year, your money could grow to be more than $,

A Higher Rate of Return Often Comes With More Risk

You may want to do whatever it takes to earn a higher rate of return on your savings or investments, but that can also be dangerous because higher rates usually bring higher what is compounding growth of an investment savings account. No matter how successful you are along the way, you'll always want to avoid the possibility of losing more than a budgeted amount of the money you invest.

To lower your risk, consider all your investment possibilities. You could start with a high-yield savings account, earning a decent amount of interest on that money year over year. There are also certificates of deposits (CDs) and money market accounts that offer you the chance to earn interest on your money. Stocks, bonds, exchange-traded funds (ETFs), index funds, and mutual funds are also investments to explore. Adding a variety of investments to your portfolio can help you diversify that risk and build your wealth through the power of compound interest.

Frequently Asked Questions (FAQs)

Compound interest is when the interest you earn on a balance in a savings or investing account is reinvested, earning you more interest. As a wise man once said, “Money makes money. And the money that money makes, makes money.”

Compound interest accelerates the growth of your savings and investments over time. Conversely, it also expands the debt balances you owe over time. Here’s everything you need to know about what Albert Einstein allegedly called the eighth wonder of the world.

What Is Compound Interest?

With compound interest, you&#;re not just earning interest on your principal balance. Even your interest earns interest. Compound interest is when you add the earned interest back into your principal balance, which then earns you even more interest, compounding your returns.

Let’s say you have $1, in a savings account that earns 5% in annual interest. In year one, you’d earn $50, giving you a new balance of $1, In year two, you would earn 5% on the larger balance of $1, which is $—giving you a new balance of $1, at the end of year two.

Thanks to the magic of compound interest, the growth of your savings account balance would accelerate over time as you earn interest on increasingly larger balances. If you left $1, in this hypothetical savings account for 30 years, kept earning a 5% annual interest rate the whole time, and never added another penny to the account, you’d end up with a balance of $4,

Interest can be compounded—or added back into the principal—at different time intervals. For instance, interest what is compounding growth of an investment savings account be compounded annually, monthly, daily or even continually. The more frequently interest is compounded, the more rapidly your principal balance grows.

Continuing with the example above, if you started with a savings account balance of $1, but the interest you earned compounded daily instead of annually, after 30 years you’d end up with a total balance of $4, what is compounding growth of an investment savings account, You would have earned an additional $ from interest being compounded more frequently.

Simple Interest vs. Compound Interest

Simple interest works differently than compound interest, what is compounding growth of an investment savings account. Simple interest is calculated based only on the principal amount. Earned interest is not compounded—or reinvested into the principal—when calculating simple interest.

Thinking in terms of simple interest, that $1, account balance that earns 5% annual interest would pay you $50 a year, period. The earned interest would not be added back into the principal. In year two, you’d earn another $

Simple interest is commonly used to calculate the interest charged on car loans and other forms of shorter-term consumer loans. Meanwhile, interest changed on credit card debt compounds—and that’s exactly why it feels like credit card debt can get so large, so quickly.

In an ideal world, you’d want your savings and investments to be calculated with compound interest—and your debts to be calculated with simple interest.

Key Compound Interest Variables

When calculating compound interest, you need to understand a few key factors. Each plays its own role in the end product, what is compounding growth of an investment savings account, and some variables can drastically impact your returns. Here are the five key variables involved in understanding compound interest:

• Interest. This is the interest rate you earn or are charged. The higher the interest rate, what is compounding growth of an investment savings account, the more money you earn or the more money you owe.
• Starting principal. How much money are you starting with? How big a loan did you take out? While compounding adds up over time, it’s all based on the initial amount you deposit or borrow.
• Frequency of compounding. The pace at which interest is compounded—daily, monthly or annually—determines how rapidly a balance grows. When taking out a loan or opening a savings account, make sure you understand how often interest compounds.
• Duration. How long do you anticipate owning an account or paying off a loan? The longer you leave what is compounding growth of an investment savings account in a savings account or the longer you hold on to a debt, the longer it has to compound and the more you’ll earn—or owe.
• Deposits what is compounding growth of an investment savings account withdrawals. Do you anticipate making regular deposits into your account? How often will you make loan payments? The pace at which you build up your principal balance or pay down your loan makes a big difference over the long run.

Compound Interest Formula

There are a few ways to calculate compound interest. The easiest way is to have an online calculator do the math for you. But sometimes it’s helpful to see the moving parts.

Here’s the compound interest formula:

A = P (1 + [r / n]) ^ nt

• A = the amount of money accumulated after n years, including interest
• P = the principal amount (your initial deposit or your initial credit card balance)
• r = the annual rate of interest (as a decimal)
• n = the number of times the interest is compounded per year
• t = the number of years (time) the amount is deposited for

It’s important to note that the annual interest rate is divided by the number of times it’s compounded a year. This gives you the daily, monthly or annual average interest rate, depending on compounding frequency.

Here’s how that plays out with numbers: Let’s say you put $5, into a savings account paying 5% interest. The account is compounded monthly for 10 years. In this situation, you know P ($5,), r (), n (12), and t (10). Now, let’s put those in the compound interest formula.

• A = P (1 + [r / n]) ^ nt
• A = 5, (1 + [ / 12]) ^ (12 * 10)
• A = 5, () ^ ()
• A = 5, ()
• A = 8,

In 10 years, you’d have about $8, in the account. That includes your $5, initial deposit and $3, in interest.

It gets trickier if you’re planning to make additional deposits to the account. You can still solve for this yourself, but it’s probably easier with Microsoft Excel.

Compound Interest Formula Excel

You can calculate compound interest in Microsoft Excel using the Future Value (FV) financial function:

=FV(rate,nper,pmt,[pv],[type])

• FV = future value
• rate = the interest rate per period
• nper = the total number of times interest is calculated
• pmt = the additional money you add each period
• pv = the present value, or the initial deposit. If you omit this, it’s assumed to be 0.
• type = either the number 0 or 1. 0 indicates payments are due at the end of the period while 1 indicates payments are due at the start of the period. If you omit this, it’s assumed to be 0.

If you leave out the pmt variable, you’ll get the same result as the first equation. To continue with the example above, here’s what would happen if you added $ a month to your initial $5, deposit:

=FV(/12,10*12,,0)

After 10 years at 5% interest, you would end up with about $23,

If you don’t want to do the math yourself, a compound interest calculator will do all of the work for you.

Simple Interest Formula

To calculate simple interest, you use a simplified version of the compound interest formula:

A = P (1 + rt)

• A = the amount of money accumulated after n years, including interest
• P = the principal amount (your initial deposit or your initial credit card bill)
• r = the annual rate of interest (as a decimal)
• t = the number of years (time) the amount is deposited for

If our $5, from before is only earning simple interest, here’s how we would calculate it:

• A = P (1 + rt)
• A = 5, (1 + [ * 10])
• A = 5, (1 + .5)
• A = 5, ()
• A = 7,

After 10 years of earning 5% simple interest, you would have $7, over $ less than if your money had been compounded monthly.

Examples of Compound Interest

Compound interest can either help or hurt you, depending on whether you’re saving or borrowing money.

• Savings accounts, checking accounts and certificates of deposit (CDs). When you make a deposit into an account at a bank that earns interest, such as a savings account, the interest will be deposited to your account and added to your balance. This helps your balance grow over time.
• (k) accounts and investment accounts. Earnings in your (k) and investment accounts also compound over time. The percentage that stocks gain from day to day are calculated based on their performance the day before, meaning they compound each business day. If you reinvest your dividends and make regular deposits, you can help your balance grow even faster.
• Student loans, mortgages and other personal loans. Compound interest works against you when you borrow. When you borrow money, you accrue interest on any money you don’t pay back. If you don’t pay the interest charges within the period stated in your loan, they’re “capitalized,” or added to your initial loan balance. After that, future interest accrues on the new, larger loan balance. Calculate how much your interest will add up to (and how much extra payments can save you) with our student loan calculator.
• Credit cards. Each month, your credit card charges interest on your balance on the card. If you never charge anything else to the card and you pay the accrued interest each month, your balance will stay the same. But if you don’t pay enough to cover the month’s new interest, it will be added to your credit card balance. Then, the next month’s interest is calculated based on that higher amount. Over time, this can cause your balance to skyrocket.

Making Compound Interest Work for You

• Give yourself time. With compound interest, the power of time is everything, what is compounding growth of an investment savings account. The sooner you start saving or investing, the longer you give that money to grow. This is why it’s important to start investing for retirement as soon as possible. The earlier you start, the less of your own money you have to save. The bulk of your retirement funds can be grown through compounding.
• Pay down debt aggressively. Compound interest works against you when you borrow money, whether that’s via student loans, credit cards or other forms of borrowing. The faster you can pay those down, the less you’ll owe over time.
• Compare APYs. The annual percentage yield, what is compounding growth of an investment savings account, or APY, will give you a better idea of what you’ll earn or be charged in interest than the annual percentage rate, or APR. That’s because the APY accounts for compounding, while the APR is the simple interest rate.

• Check the rate of compounding. The more frequently an account compounds interest, the more you’ll earn. (Or the more you’ll owe.) Ideally, you want your savings products to compound as frequently as possible and your debts to compound as infrequently as they can.

The Bottom Line

Compound interest and compounding can what is compounding growth of an investment savings account your savings and retirement potential. Successful compounding lets you use less of your own money to reach your goals. However, compounding can also work against you, like when high-interest credit card debt builds on itself over time. That’s why compounding is a powerful motivator to pay off your debts as soon as you can and start investing and saving your money early.

Legend has it that the physics genius, Albert Einstein, once described the mathematical rule of ‘compounding’ – a vital ingredient for successful, long-term saving and investing - as the ‘eighth wonder of the world’.

Here’s why you should try and harness its power for your investments.

How what is compounding growth of an investment savings account works

Compound can turbocharge your returns – so long as you have plenty of time on your side.

If you invest £10, and it returns 2% income after the first year, you will see £ added to your investment pot.

In the second year as well as earning returns on your original £10, you also earn on the £ growth. Should the rate of return remain at 2%, your investment of £10, would grow by £ of income the next year giving a total of £10,

In subsequent years, the same formula applies, meaning your money grows at a faster rate by leaving the income invested.

With our theoretical example of £10, saved, a person who withdrew their 2% each year would see just £2, added to their original balance after 10 years, compared to a compound investor that would have had nearly £2, added.

After 20 years, assuming the same growth, your original balance would rise to £14, That’s £ more than if you had received returns only on your original sum.

The power of compounding

As long as you are patient and have plenty of time before you need to tap into your investments, you should benefit from the snowball effect of compound growth as the years roll by.

This principle applies to money held in bonds that pay annual interest, shares that pay dividends (the share of company profits distributed to investors), and funds that can pay either depending on what the fund is what is compounding growth of an investment savings account in.

Many companies pay dividends quarterly or half yearly which means that compounding can get to what is compounding growth of an investment savings account more quickly. The majority of funds pay out twice each year.

Reinvest those returns rather than take them as income, what is compounding growth of an investment savings account, and the growth will compound. This means you’ll see your money grow – as long as positive markets mean the income being earned continues over the long term.

Consider the mathematical Rule of 72 as a rough guide to how compounding can work for you. Divide 72 by your selected annual income rate to get the number of years it should take to double your money. In our example, 72 divided by 2 equals 36 years.

Our figures don’t take into account the impact of markets on the original £10, invested which will hopefully also be rising over the years, though this is not guaranteed and it could fall in value.

The compounding sums in our illustration do not reflect the impact of inflation – the rising cost of living over time, which reduces the spending power of your money. Nor do they take account of any tax you might owe on returns or costs you may need to pay for holding your investment.

Further, when it comes to dividends, those companies that pay dividends may cut, delay or even cease them in economically challenging periods.

But by compounding the returns over the longer term you can potentially help your money work harder without lifting a finger.

By investing in a fund and selecting to buy accumulation units (rather than income units), the growth will compound without you having to do anything. The earlier you start saving and investing, the sooner you could start to earn interest or dividends (so long as companies pay them) and start seeing compounding work for you.

Compounding is a powerful investing concept that involves earning returns on both your original investment and on returns you received previously. For compounding to work, you need to reinvest your returns back into your account. For example, you invest $1, and earn a 6% rate of return. In the first year, you would make $60, bringing your total investment to $1, if you reinvest your return.

Next year, you would earn a return on your total $1, investment. If your return were once again 6%, you’d make $, bringing your total investment to $1,

Over the long term, compound growth can multiply your initial investment exponentially. In our hypothetical example, if your return stayed at 6%, by year 30, your annual earnings would be $ That’s more than five times the $60 return you earned the first year — just for what is compounding growth of an investment savings account by and letting your money grow.

Make compound growth work for you

Take the effort out of compounding by reinvesting your earnings automatically. In turn, those earnings add to the value of your account and boost the potential to earn even more. The key? Patience. Don't be tempted to withdraw the funds when they grow. Keep in mind that if you hold your investments in a taxable account, you'll still be taxed on the interest, dividends, and capital gains you receive, even if you reinvest them into the account.

Want to help build your money faster? Add new money to the account regularly. Your financial services provider can help you establish such an automatic transfer easily, or your employer might offer the option to do so with a split direct deposit.

Compounding relies on the power of time. Start saving and investing early — either in an account that earns interest or invest bitcoin and earn an investment that pays dividends that can be reinvested.

What Is Compounding?

Compounding is the process in which an asset’s earnings, from either capital gains or interest, are reinvested to generate additional earnings over time. This growth, calculated using exponential functions, occurs because the investment will generate earnings from both its initial principal and the accumulated earnings from preceding periods.

Compounding, therefore, differs from linear growth, where only the principal earns interest each period.

Understanding What is compounding growth of an investment savings account

Compounding typically refers to the increasing value of an asset due to the interest earned on both a principal and accumulated interest. This phenomenon, which is a direct realization of the time value of money (TMV) concept, is also known as compound interest. 

Compound interest works on both assets and liabilities. While compounding boosts the value of an asset more rapidly, it can also increase the amount of money owed on a loan, as interest accumulates on the unpaid principal and previous interest charges.

To illustrate how compounding works, suppose $10, is held in an account that pays 5% interest annually. After the first year or compounding period, the total in the account has risen to $10, a simple reflection of $ in interest being added to the $10, principal. In year two, the account realizes 5% growth on both the original principal and the $ of first-year interest, resulting in a second-year gain of $ and what is compounding growth of an investment savings account balance of $11, After 10 years, assuming no withdrawals and a steady 5% interest rate, the account would grow to $16,

Special Considerations

The formula for the future value (FV) of a current asset relies on the concept of compound interest. It takes into account the present value of an asset, the annual interest rate, the frequency of compounding (or the number of compounding periods) per year, and the total number of years. The generalized formula for compound interest is:

​FV=PV×(1+i)nwhere:FV=Future valuePV=Present valuei=Annual interest raten=Number of compounding periods per year​

Increased Compounding Periods

The effects of compounding strengthen as the frequency of compounding increases. Assume a one-year time period. The more compounding periods throughout this one year, the higher the future value of the investment, so naturally, two compounding periods per year are better than one, and four compounding periods per year are better than two.

To illustrate this effect, consider the following example given the above formula. Assume that an investment of $1 million earns 20% per year. The resulting future value, based on a varying number of compounding periods, is:

• Annual compounding (n = 1): FV = $1, × [1 + (20%/1)] ^{(1 x 1)} = $1,
• Semi-annual compounding (n = 2): FV = $1, × [1 + (20%/2)] ^{(2 x 1)} = $1,
• Quarterly compounding (n = 4): FV = $1, × [1 + (20%/4)] ^{(4 x 1)} = $1,
• Monthly compounding (n = 12): FV = $1, × [1 + (20%/12)] ^{(12 x 1)} = $1,
• Weekly compounding (n = 52): FV = $1, × [1 + (20%/52)] ^{(52 x 1)} = $1,
• Daily compounding (n = ): FV = $1, × [1 + (20%/)] ^{( x 1)} = $1,

As evident, the future value increases by a smaller margin even as the number of compounding periods per year increases significantly. The frequency of compounding over a set length of time has a limited effect on an investment’s growth. This limit, based on calculus, is known as continuous compounding and can be calculated using the formula:

​FV=P×ertwhere:e=Irrational number r=Interest ratet=Time​

In the above example, the future value with continuous compounding equals: FV = $1, × ^{( x 1)} = $1,

Example of Compounding

Compounding is crucial in finance, and the gains attributable to its effects are the motivation behind many investing strategies. For example, many corporations offer dividend reinvestment plans (DRIPs) that allow investors to reinvest their cash dividends to purchase additional shares of stock, what is compounding growth of an investment savings account. Reinvesting in more of these dividend-paying shares compounds investor returns because the increased number of shares will consistently increase future income from dividend payouts, assuming steady dividends.

Investing in dividend growth stocks on top of reinvesting dividends adds another layer of compounding to this strategy that some investors refer to as double compounding. In this case, not only are dividends being reinvested to buy more shares, but these dividend growth stocks are also increasing their per-share payouts.

Let’s take a quick walk down memory lane—to algebra class. Do you remember learning about exponential growth? You have an equation to work out, and then you map a curved line on some graph paper. It starts out low and gradual, but when it finally takes off, it skyrockets! 

If this sounds like Charlie Brown’s teacher right now (wa-waa-waa-waaa), hang with us. Exponential growth explains how compound interest works, and—if you use it right—this powerful formula could make you millions of dollars.

So, let’s jump right in: What is compound interest and how does it work?  

What Is Compound Interest?

Compound interest is earning interest on top of interest. When you invest money, you’re expecting to get a return on your money, meaning that you should end up with more money than you originally put in. If you leave that money alone (the initial principal plus the interest), compound interest applies the interest rate to the total new amount of money earned, so that it builds exponentially over time.  

Simple interest, on the other hand, does not accrue (fancy investing talk for build up over time). Once you pay (or earn) interest for a particular period, it’s gone. It’s not added to the next payment period the way compound interest is. 

Compound interest is the secret sauce for building wealth, and it’s one of the most basic principles of investing. If you want to build wealth, you have to get out of debt (paying interest) and start investing (earning interest).

How Does Compound Interest Work?

Compound interest is like a snowball that’s rolling downhill. As it picks up momentum over time, it gets bigger and bigger. Here’s an example:

Let’s say you invest $1,, and—just to keep it simple—it earns 10% a year in interest. After one year, you’d have $1,—the original money plus $ interest that you earned. The second year, you’d have slightly more—$1,—because you’re earning interest on top of interest. The investment compounds, or builds up, over time. Now $1, doesn’t seem like a big deal at first, but it becomes a big deal later. If we leave that $1, alone for 40 years, and it compounds annually at 10%, it will grow to a sum of over $53,! And all you put in was $1,!

The number of compounding periods will determine how quickly your investment grows. Interest can be compounded daily, weekly or yearly.

Compound Annual Growth Rate (CAGR)

Compound Annual Growth Rate is an important investment concept that’s related to compound interest. It’s a way to measure the growth rate of your investments over time. When you’re investing to save for retirement, you should put your money in mutual funds. Mutual funds don’t earn a fixed interest rate. In fact, the value of a mutual fund can rise and fall. That’s why it’s important to choose mutual funds with a long history of strong returns.

When estimating the overall growth of mutual fund investments, some people use the long-term growth rate of the S&P The S&P is a common measuring stick for how the stock market is performing. 

The Power of Compounding

To help you see the power of compounding in action, here's the story of Jack and Blake—two guys who got serious about investing for retirement. They picked good, growth stock mutual funds that average an annual return of about %—just under the long-term growth rate of the S&P

Jack

• Starts investing at age 21
• Invests $2, every year
• Stops contributing money at age 30
• Total amount contributed: $21,

Blake

• Starts investing at age 30
• Invests $2, every year
• Contributes money until age 67 (a total of 37 years!)
• Total amount contributed: $91,

At age 67, Jack’s investment has grown to $2,,, and Blake’s has grown to $1,,! Nine years made a difference of over one million dollars.

So, while mutual fund investments don’t earn compound interest, they do experience compound growth—and as you can see, it works the same way! The secret sauce for harnessing the power of compound interest is time. The number of compounding periods is what makes your interest explode.

Compound Interest Formula

All right, math nerds, it’s your time to shine. Here’s how you calculate compound interest:

A = P(1+r/n)^nt

• P is the principal (starting amount)
• r is the interest rate
• n is the number of times the interest compounds each year
• t is the total number of years your money is invested
• A is your final amount

If you’re experiencing terrifying flashbacks to school days when you had to memorize math formulas for a test, don’t worry. We’ve got a compound interest calculator that will do the calculations for you.

How to Grow Your Investments With Compound Interest

The combination of compound interest (or growth) and time is the key to investing. But it won’t make you rich overnight. It’s all about having the right mindset. Stay focused for the long haul. Be disciplined. It will pay off in the end!

Remember: Interest that you pay is a penalty. Interest that you earn is a reward. Here are four key strategies to get your money working for you in compound interest:

1. Get out of debt.

Compound interest is a powerful force. You want it to work for you, not against you. If you’re in debt, you might be making compounding interest payments on a credit card. That’s why it feels like drowning—because the amount you owe keeps increasing. Avoid debt like the plague. Check out the debt snowball for a proven plan to destroy your debt—for good.

2. Start as soon as possible.

Remember Jack and Blake? The more compounding periods your money experiences, the larger it will grow. Start investing in growth stock mutual funds (either through your workplace retirement plan or a Roth IRA) as soon as you can.

3. Increase your contributions each year.

If you get a raise this year, earn some money through a side hustle, or come into some money through an inheritance, increase your contributions instead of increasing your standard of living. You should invest at least 15% of your income in retirement, and there are ways to invest more than 15% as your earnings increase. It will be worth it when you watch your investments explode.

4. Exercise patience.

Have a long-term mindset. The key to harnessing the power of compound interest is to leave your money alone for an extended amount of time. For the first few years, it might feel like nothing’s happening. But remember that exponential growth graph we talked about earlier? The longer you let it be, the higher it grows!  

It’s great to save money and build wealth, but what’s it all for? The whole point of understanding the power of compound interest is to be able to invest and reach your high definition retirement dreams. If you haven’t started planning for your financial future, reach out to an investing professional to help you get started. Our SmartVestor Program will connect you with qualified investing professionals in your area who can take a look at where you are and help you create a plan you can get started on.

Find a SmartVestor Pro in your area today!

Not only can the passage of time help lower your investment risk, it can potentially increase the rewards of investing.

Imagine you place 1 checker on the corner of a checker board. Then you place 2 checkers on the next square and continue doubling the number of checkers on each following square.

If you've heard this brainteaser before, you know that by the time you get to the last square on the board&#;the 64th&#;your board will hold a total of 18,,,,,, checkers.

No, we're not promising to double your money every year! But this principle&#;known as "compounding"&#;is important to understand: When your starting amount is higher, your increases are higher too. And over time, it can seriously add up.

As a rule of thumb, if your investments returned 6% annually, you would double your investment about every 12 years.

For example, if you earn 6% on a $10, investment, you'll make $ in the first year. But then you start the second year with $10,&#;during which your 6% returns net you $

In the 20th year of this hypothetical example, you'll earn more than $1,&#;and your balance will have increased more than %.

Editorial Note: Credit Karma receives compensation from third-party advertisers, but that doesn’t affect our editors’ opinions. Our third-party advertisers don’t review, approve or endorse our editorial content. It’s accurate to the best of our knowledge when posted.

One of the best parts of opening a savings account is watching the money you deposit grow over time, thanks to interest.

Savings accounts typically grow with compound interest — that means you earn interest both on the amount you’ve saved and any interest you previously accrued.

Let’s take a look at how compound interest works and factors that can affect how quickly your money grows.

1. What is compound interest on a savings account?
2. How often does a savings account compound interest?
3. How do you calculate compound interest?
4. Factors that affect how much interest you earn
5. What&#;s next?

What is compound interest on a savings account?

You may have heard of interest on a credit card or car loan — that’s the cost of borrowing money from a bank or lender — and it’s expressed as a rate.

On the flipside, when financial institutions borrow money from you, they pay you interest. They typically pay interest on deposit accounts — such as savings accounts, checking accounts and money market accounts — in exchange for the ability to use your money until you need it.

Savings accounts can earn interest one of two ways: through simple interest or compound interest. With simple interest, you earn interest only on your principal — the amount you’ve deposited into your account.

But compound interest allows you to earn interest on your principal and the interest you’ve already earned.

Let’s say your bank compounds interest on your account every month. After the first month, the bank pays interest on the principal. The next month, the bank pays interest on the principal plus the previous interest you earned. From there, the interest continues to accumulate each month on the combined amount of your savings and interest earned.

In general, you’ll earn more on an account with compound interest than on one with simple interest.

How often does a savings account compound interest?

Depending on your financial institution and the account, interest can compound daily, monthly, quarterly or annually. The more often interest compounds, the faster your balance will grow.

The amount of interest you earn each year, based on the total amount of interest earned and how often interest is compounded, is expressed as the annual percentage yield, or APY. The more frequently interest is compounded, the higher your APY — and therefore, your interest earnings — will be.

How do you calculate compound interest?

An online compound interest calculator can help you crunch the numbers, but you can also do the math yourself. Here’s the equation for calculating compound interest.

Here’s an example to help you figure out the future value of your savings account.

Let’s say you open an account with an initial deposit of $2, (this is your principal, or P). If your annual interest rate is 2%, then R = . If your bank compounds interest once a month, N =12 here. Let’s say you want to calculate how much you’d have in savings after two years (T = 2).

Your calculation would look like this.

A = 2,(1+ /12)^{(12 x 2)}

At the end of two years — assuming you haven’t withdrawn or made any deposits to the account — you’d have $2, Your original deposit was $2,, so you would’ve earned $ in interest.

Factors that affect how much interest you earn

A range of factors can influence how much interest you can earn — and how quickly you earn it. Here are a few.

The amount of money in your account

Generally, the more money you have in your savings account, the more interest you’ll earn over time. Making recurring deposits means you’ll earn interest on a larger balance, while withdrawing money means you’ll accrue interest on a smaller balance. In other words, it pays to keep the money in your account.

Your interest rate

Your APY may change over time, especially if the Federal Reserve raises or lowers the federal funds rate, so be sure to pay attention to any rate changes.

How frequently your financial institution compounds interest will affect how much you earn, too — another reason why comparing APYs across savings accounts is important.

Account fees

While account fees won’t change the amount of interest you earn, they could offset your earnings — or, worse yet, you could end up paying more in fees than you earn in interest. Depending on the institution and the account, you might pay a monthly maintenance fee or fees for exceeding your withdrawal limit, requiring overdraft protection or using an ATM, among others. Banks usually offer workarounds to avoid some monthly fees, such as keeping a minimum balance, so read all the terms before opening an account.

What’s next?

Whether you’re saving for a car down payment, building an emergency fund or working toward another savings goal, a savings account with compound interest could be a good place to stash your money. The interest works in your favor, and you can access the funds in a pinch.

To help find the best savings account for your financial goals, shop around and compare APYs and terms from a range of institutions. Keep in mind that some online banks may offer higher rates than brick-and-mortar banks or credit unions.

You might also consider a high-yield savings account, which offers a higher interest rate than traditional savings accounts. Just make sure the bank, credit union or other depository institution is insured by the FDIC or NCUA, and pay attention to the fine print, such as minimum deposit or balance requirements, how often the interest compounds, and any fees — details that can affect your rate of return in the long run.

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Compounding is a powerful investing concept that involves earning returns on both your original investment and on returns you received previously. For compounding to work, you need to reinvest your returns back into your account. For example, you invest $1, and earn a 6% rate of return. In the first year, you would make $60, bringing your total investment to $1,, if you reinvest your return.

Next year, you would earn a return on your total $1, investment. If your return were once again 6%, you’d make $, bringing your total investment to $1,

Over the long term, compound growth can multiply your initial investment exponentially. In our hypothetical example, if your return stayed at 6%, by year 30, your annual earnings would be $ That’s more than five times the $60 return you earned the first year — just for sitting by and letting your money grow.

Make compound growth work for you

Take the effort out of compounding by reinvesting your earnings automatically. In turn, those earnings add to the value of your account and boost the potential to earn even more. The key? Patience. Don't be tempted to withdraw the funds when they grow. Keep in mind that if you hold your investments in a taxable account, you'll still be taxed on the interest, dividends, and capital gains you receive, even if you reinvest them into the account.

Want to help build your money faster? Add new money to the account regularly. Your financial services provider can help you establish such an automatic transfer easily, or your employer might offer the option to do so with a split direct deposit.

Compounding relies on the power of time. Start saving and investing early — either in an account that earns interest or with an investment that pays dividends that can be reinvested.

It is rumored that Albert Einstein once quipped that the most powerful force in the universe is the principle of compounding. In investing and finance, this force manifests itself through the concept of compounding returns. In simple terms, compound interest means that you begin to earn interest on the interest you receive, which multiplies your money at an accelerated rate.

For example, if you have $ and earn 10% interest per year, you will have $ after one year. Then, if you earn 10% interest the next year on that $, you end up with $ by the end of year two. The process continues until, eventually, your original $ may be eclipsed by the amount of interest you gained.

This is one way many top investors find success in building their wealth. But it's not just for the top investors—you can take advantage of compound interest through savings accounts and investment portfolios. Learn how to do that below.

What Determines How Much Compound Interest You Can Earn?

There are three main factors that can influence the rate at which your money compounds:

1. The rate of return, or the profit, on your investment: For example, if you are investing in dividend-paying stocks, this would be your total profit from capital gains and dividends. If you were putting money in a savings account, this would be the annual percentage yield (APY).
2. Time:The more time you give your money to build upon itself, the more it compounds. For example, all things equal, your money would grow more over a year period than it would over a five-year period.
3. The tax rate, and when you have to pay taxes on your interest:You will end up with far more money if you don’t have to pay taxes at all, or at least not until the end of the compounding period rather than at the end of each year. This is why tax-deferred accounts, such as the traditional IRA, Roth IRA, (k), and SEP-IRA, are so important to consider.

Compound Interest and the Time Value of Money

The foundation behind compounding interest is the concept of the time value of money, which states that the value of money changes, depending upon when it is received. Having $ today is preferable to receiving it a few years from now because you can invest it to generate dividends and interest income. Compounding allows that money to grow. If you waited two years to receive that $, you'd miss out on two years of opportunity to earn compound interest. This is known as opportunity cost.

Opportunity cost is the loss of possible gains if an action is not chosen. In this case, the opportunity cost is equal to the amount of money you do not get in interest if you don't invest in that money.

In our earlier example, if you don't invest the $ in an account with 10% annual interest, you'll lose the opportunity to earn $50 or more per year in interest. In 10 years, your $ could be $1, But if you don't invest it, it'll still be $ 10 years later.

When you understand the time value of money, you'll see that compounding and patience are the ingredients for building wealth.

Here's another example: Let's say you are 30 years old and want to have $1 million by the time you retire at age You can afford to save $ per month in an account with an 8% annual return on your investment. Will you be able to reach your goal? Using a compound interest calculator, you can see that you'd be able to turn that $ per month into $1 million after 29 years—six years earlier than you plan on retiring.

Compound Interest Results Over Time

Another way to understand the power of compound interest is to put values into a compound interest table that shows you just how much your wealth can multiply over time.

Imagine you're an investor who sets aside a lump sum of $10, Take a look at the table below to see the influence of time and different rates of return on this investment. Over time, saving money is not the only key to a large fortune; compound interest plays a big part.

For instance, a year-old who invests $10, today and parks it in Treasury bills, earning 4% per year, on average, for the next 50 years, will have $71,, if the purchases were made through ​a tax-free account such as a Roth IRA. If they had invested in stocks and real estate, earning a 12% average annual rate of return over the same time, they would end up with $2,, Adding asset classes with higher returns would result in over 40 times more money, thanks to the power of compounding.

How Compound Interest Could Impact Teens and Their Savings

Your teenage years are a good time to start saving money for the future. Because you have time for that money to grow before you may need it to buy a house or retire, you can benefit greatly from compound interest. One easy way to start earning compound interest is to open a high-yield savings account and contribute a set amount to it every month. Over time. your money could grow a lot and allow you to build your wealth. While you may only be able to earn a small amount of interest in a savings account, the compound interest could add up over time. For example, if you contributed $50 per month to a high-yield savings account and earned % interest per year, you could have over $12, after 20 years.

Once you've got the savings part down, you could try your hand at investing to potentially benefit even more compound interest. For example, let's say you opened an investment account with the help of an adult (you usually need to be 18 years or older to invest). If you contributed $ per month to the investment account for 40 years, and earned a 10% annual rate of return on investment each year, your money could grow to be more than $,

A Higher Rate of Return Often Comes With More Risk

You may want to do whatever it takes to earn a higher rate of return on your savings or investments, but that can also be dangerous because higher rates usually bring higher risk. No matter how successful you are along the way, you'll always want to avoid the possibility of losing more than a budgeted amount of the money you invest.

To lower your risk, consider all your investment possibilities. You could start with a high-yield savings account, earning a decent amount of interest on that money year over year. There are also certificates of deposits (CDs) and money market accounts that offer you the chance to earn interest on your money. Stocks, bonds, exchange-traded funds (ETFs), index funds, and mutual funds are also investments to explore. Adding a variety of investments to your portfolio can help you diversify that risk and build your wealth through the power of compound interest.

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