Compound Interest Formula Explained

Last Updated on

compound interest formula calculatorA key component of successful investing is understanding the “magic” of compound interest. Of course, there’s nothing magical about it: just a mathematical compound interest formula that determines how much — and how quickly — your money will grow. Here’s everything you need to know about compound interest, as well as how to use a compound interest calculator to help you select the best investments to achieve your financial goals.

How Compound Interest Works

Most people are familiar with the concept of earning interest on savings: a bank or other financial institution pays you at a specified rate for the privilege of accessing your money. What’s special about compound interest is that you don’t only earn money on your initial deposits or principal, but also on any interest you’ve already accumulated.

In other words, you earn interest on your interest, which can snowball over time. How quickly that snowball grows depends on the rate of interest and the compounding interval (e.g., daily, weekly, monthly, quarterly, semi-annually or annually).

A good point of reference is the rule of 72, which tells you how many years it takes to double your investment when interest is compounded annually. Simply divide 72 by the interest rate to get the answer in years. So, for example, with an annual interest rate of 6%, it would take 12 years to double your investment.

Simple Interest vs. Compound Interest

Unlike compound interest, simple interest is calculated and paid on the principal investment and deposits only. The interest you earn is not automatically added to your principal amount, and so you do not achieve any of the benefits of compounding.

In our example above, you would earn a total of just $24,840 in simple interest at the end of the 10-year period, a substantial difference of $4,346 compared with annual compound interest earnings.

Taking Advantage of Compound Interest

There are several ways to maximize the effects of compound interest:

  • Start investing early. The sooner you begin to earn money on your investments, the more time you will have to let those earnings compound and grow.
  • Invest for the long term. Holding on to your investments for as long as you can will also allow as much time as possible for the compounding effect.
  • Make regular contributions. Instead of waiting until the end of the year to invest, contribute throughout the year to start earning interest right away — and so those interest payments can begin compounding.
  • Think about your interest rate/rate of return. If you aren’t earning much in interest or if high management fees are cutting into your investments’ rate of return, you won’t enjoy the same benefits of compounding as you would with a higher rate.

Compound Interest Formula

It’s easiest to use an online compound interest calculator, but if you’re a math whiz, you can calculate it yourself:

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

A = value after t periods

P = principal amount (initial investment)

r = annual nominal interest rate (not reflecting the compounding)

n = number of times the interest is compounded per year

t = number of years the money is borrowed for

This is one way to figure out the results of the annual compound interest.

Compound Interest Calculator

Rather than using pen and paper, you can use a compound interest calculator to help you find out how your investment will grow over time. Compound interest calculators allow you to input values for the initial investment, regular contributions, interest rate, compounding intervals and the number of years invested to see how various circumstances will affect your outcome.

Say, for example, you were to make an initial deposit of $15,000 and then contribute $400 per month ($4,800 per year) at an annual interest rate of 6% compounded annually. Using a compound interest calculator, you would find that after 10 years your savings will have grown to $92,186.74, including $63,000 in deposits, and $29,186.74 in total interest income, as shown in the table below.

Interest compounded monthly at 6%
YearDepositInterestBalance
Start$15,000n/a$15,000
1$4,800$1,056.00$20,856.00
2$4,800$1,407.36$27,063.36
3$4,800$1,779.80$33,643.16
4$4,800$2,174.59$40,617.75
5$4,800$2,593.07$48,010.82
6$4,800$3,036.65$55,847.47
7$4,800$3,506.85$64,154.31
8$4,800$4,005.26$72,959.57
9$4,800$4,533.57$82,293.15
10$4,800$5,093.59$92,186.74
Total$63,000$29,186.74$92,186.74

Comparing Investments with a Compound Interest Calculator

By using a compound interest formula calculator, you can easily compare different investments based on the expected rate of interest, how frequently the returns are compounded, and your time horizon.

Here’s an example:

 Investment #1Investment #2Investment #3Investment #4
Starting balance$2,500$2,500$2,500$2,500
Monthly deposit$0$0$0$0
Annual interest rate5%5%5%6%
Compounding intervalYearlyMonthlyYearlyYearly
Number of years to grow35354035
Final balance$13,790.04$14,334.30$17,599.97$19,215.22

In each case, just one element varies from Investment #1, yet the final balance is different every time. Clearly, changing just one variable — such as the compounding interval, interest rate or the number of years an investment is held — will impact your final balance.

Using a compound interest calculator will help you evaluate which investment will give you the best returns.

Compounding Intervals

Another way to take advantage of compound interest is to choose the most frequent compounding interval offered.

Interest can be compounded annually, as shown in the table above, or on shorter intervals including semi-annually, quarterly, monthly, weekly. You can even use a daily compound interest formula. The shorter the interval, the larger the resulting balance.

If we revisit our example, here’s how the same investment ($15,000 initial deposit and $400 contributed monthly) would add up after 10 years, with the same annual interest rate of 6% but at different compounding intervals:

INTERVALCOMPOUND INTEREST FORMULAFINAL BALANCETOTAL
INTEREST
AnnuallyCompounded once per year at 6%$92,186.74$29,186.74
Semi-annuallyCompounded every 6 months at 3%
(6% a year divided by 2)
$92,709.12$29,709.12
QuarterlyCompounded every 3 months at 1.5%
(6% a year divided by 4)
$92,982.96$29,982.96
MonthlyCompounded every month at 0.5%
(6% a year divided by 12)
$93,170.45$30,170.45
DailyCompounded each day at 0.0164%
(6% a year divided by 365)
$93,502.07$30,502.07

As illustrated, when the compounding interval is shorter, you earn more interest and therefore end up with a larger balance, even when the total deposits ($63,000) and annual interest rate (6%) are the same.

Final Word

Compound interest can significantly boost investment returns over the long term, especially when dealing with larger sums. A $100,000 investment earning 5% simple interest, for example, would give you $50,000 in interest over 10 years; $62,889.46 over the same period when interest is compounded annually; or $66,015.21 when interest is compounded daily. Understanding how the compounding interval and rate of interest affect your returns will help you choose the right investments for your financial needs.

The following two tabs change content below.
Tamar Satov

Tamar Satov

Tamar Satov is an award-winning journalist specializing in the areas of personal finance and parenting. Her work has appeared in Canadian Living, The Globe and Mail, Today’s Parent, Parents Canada, Walmart Live Better and many other consumer magazines and websites. She is the former Managing Editor of CPA Magazine, for Canada’s Chartered Professional Accountants, and contributes to other publications for finance professionals including FORUM, for Canada’s financial advisors.
Tamar Satov

Latest posts by Tamar Satov (see all)

Leave a Comment





> >