How to Calculate Compound Interest (Formula and Example)
Short answer. Multiply the principal by (1 + r/n) raised to the power n x t, where r is the annual rate, n the compounding periods per year and t the years. $10,000 at 5% compounded yearly for 10 years grows to about $16,289; interest earned is the final amount minus the principal.
The formula
A = P x (1 + r/n)^(n x t)
Step by step
- Define the inputs. P is the starting amount, r the annual rate as a decimal, n compounding periods per year, t years.
- Compute the periodic rate. r divided by n.
- Compute the number of periods. n multiplied by t.
- Raise to the power. (1 + periodic rate) to the number of periods, then multiply by P.
- Subtract P for interest. A minus P is the interest earned.
Worked example
$10,000 at 5% for 10 years
- Yearly compounding: 10,000 x 1.05^10 = $16,288.95.
- Monthly compounding: 10,000 x (1 + 0.05/12)^120 = $16,470.09.
- Rule of 72 check: 72 / 5 = 14.4 years to double, so about 1.6x after 10 years is consistent.
Common mistakes
- Entering the rate as 5 instead of 0.05.
- Forgetting to multiply n by t in the exponent.
- Comparing a nominal rate with an effective annual rate.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is earned only on the principal; compound interest is earned on the principal plus previously earned interest.
Does more frequent compounding matter?
It increases the result, but with diminishing returns: monthly versus daily compounding differs very little.
How can I estimate doubling time quickly?
Divide 72 by the annual rate in percent. See the Rule of 72.
General education, not personal financial advice. Example figures are illustrative.