How to Calculate Compound Interest

With compound interest, the interest you earn is added to the balance, and the next round of interest is calculated on the larger amount. Over long periods this makes a large difference.

The formula

A = P × (1 + r ÷ n)^(n × t)

A = final amount
P = starting amount (principal)
r = annual interest rate as a decimal
n = compounding periods per year
t = number of years

Example

Invest 10,000 at 7% a year, compounded once a year, for 20 years.

A = 10,000 × 1.07^20 = 38,696.84

That is 28,696.84 of interest. Simple interest on the same amount would add only 7% of 10,000 each year, so 24,000 in total, which is 14,696.84 less.

Compounding frequency

More frequent compounding at the same annual rate gives a little more, but the gain shrinks quickly. For the same 10,000 at 7% over 20 years:

Moving from monthly to daily adds less than 160 over 20 years.

Adding regular deposits

Putting in 200 a month at 7% a year, compounded monthly, for 20 years gives about 104,185. You would have deposited 48,000, so about 56,185 is interest.

The Rule of 72

Divide 72 by the annual rate to estimate the years needed to double. At 7%, 72 ÷ 7 is about 10.3 years. The exact figure is 10.24 years. The rule is a quick estimate that works best for rates between about 4% and 12%.

Common mistakes

• Entering the rate as 7 instead of 0.07 in the formula.
• Ignoring inflation, taxes and fees, all of which reduce the real return.
• Treating a projection as a promise. Real returns vary from year to year.

The compound interest calculator adds monthly contributions and a year-by-year table.

Try it yourself

1. What is 5,000 worth after 3 years at 4% a year, compounded yearly?
2. Use the Rule of 72 to estimate the doubling time at 9%.
3. Compare 1,000 for 2 years at 6% with yearly compounding and with simple interest.

Answers: (1) 5,624.32; (2) About 8 years (72 ÷ 9); (3) 1,123.60 compound against 1,120 simple.