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%|
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 #1||Investment #2||Investment #3||Investment #4|
|Annual interest rate||5%||5%||5%||6%|
|Number of years to grow||35||35||40||35|
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.
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:
|INTERVAL||COMPOUND INTEREST FORMULA||FINAL BALANCE||TOTAL |
|Annually||Compounded once per year at 6%||$92,186.74||$29,186.74|
|Semi-annually||Compounded every 6 months at 3%|
(6% a year divided by 2)
|Quarterly||Compounded every 3 months at 1.5%|
(6% a year divided by 4)
|Monthly||Compounded every month at 0.5%|
(6% a year divided by 12)
|Daily||Compounded each day at 0.0164%|
(6% a year divided by 365)
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.
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.