How Compound Interest Works and the Rule of 72
Compound interest means you earn interest on your original money and also on the interest added earlier. Over long periods this makes a big difference.
Formula
A = P x (1 + r)t, where P is the starting amount, r is the interest rate per period and t is the number of periods.
Simple versus compound
Take 100,000 at 10 percent per year for 3 years. With simple interest you earn 10,000 each year, giving 130,000. With compound interest the amount grows to 110,000, then 121,000, then 133,100. The extra 3,100 comes from interest earning interest.
The Rule of 72
Divide 72 by the annual rate to estimate how many years it takes to double your money. At 8 percent, 72 / 8 = 9 years. It is an estimate, but it is handy for quick decisions.
Why starting early matters
Time is the strongest factor. Money invested for 30 years has far more time to compound than the same money invested for 10 years, even at the same rate.
A word of caution
Compounding works against you with debt too, such as credit cards. Also, real investment returns can vary, so a fixed rate is only an assumption.
Why compounding frequency matters
Interest can be added yearly, monthly or even daily. At 10 percent per year, 100,000 grows to 110,000 after one year with yearly compounding, but to about 110,471 with monthly compounding. The difference is small in one year but grows with time.
Regular contributions
Adding money every month makes compounding stronger. Saving 10,000 at the end of each month at 1 percent monthly growth gives about 126,825 after 12 months, although you only deposited 120,000.
Look at the real return
Inflation reduces what your money can buy. If your savings earn 8 percent and prices rise 6 percent, your real growth is only around 2 percent. Always compare returns with inflation.
Frequently asked questions
How often do banks compound interest?
It depends on the product. Some compound daily or monthly, others quarterly or yearly. Check the terms of your account.
Is the Rule of 72 exact?
No. It is an approximation that works best for rates between about 6 and 10 percent.
Test different numbers with our Compound Interest Calculator.