Calculate compound interest growth over time. See how your investment grows with monthly, quarterly, or annual compounding.
The compound interest formula is: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of times interest compounds per year, and t is time in years.
Example: $10,000 invested at 7% compounded monthly for 20 years: A = 10,000 × (1 + 0.07/12)^(12×20) = 10,000 × (1.00583)^240 = $40,170. The $30,170 gain is pure compound growth on the original $10,000.
Compounding frequency matters: Daily compounding grows slightly faster than monthly, which grows faster than annual. At 7% for 10 years on $10,000: Annual = $19,672 · Monthly = $20,097 · Daily = $20,136. The difference between daily and monthly is small, but it adds up over decades.
Divide 72 by the annual interest rate to estimate how many years it takes to double your money: 72 ÷ 7% = 10.3 years. At 10%: 72 ÷ 10 = 7.2 years.
Compound interest applies the formula A = P(1 + r/n)^(nt), where P is principal, r the annual rate, n compounding periods per year and t years. Interest earned in each period joins the principal, so growth accelerates over time — the effect Einstein allegedly called the eighth wonder of the world.
$10,000 at 7% compounded annually becomes $19,672 in 10 years and $76,123 in 30 years. The last decade alone adds more than the first two combined — that is the power of exponential growth.
What is the Rule of 72? Divide 72 by the interest rate to estimate doubling time: at 8%, money doubles roughly every 9 years.
Simple vs compound interest? Simple interest pays only on principal; $10,000 at 7% simple earns $700 every year, while compounding earns increasingly more each year.
Continuous compounding? The theoretical maximum, A = Pe^(rt), only slightly outpaces daily compounding at typical rates.