Compound Interest Formula Explained
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.
Rule of 72
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.
Frequently Asked Questions
What is the difference between compound and simple interest?+
Simple interest is always calculated on the original principal only. Compound interest is calculated on principal plus all previously earned interest. On $10,000 at 6% for 20 years: simple interest = $22,000 total; compound (annual) = $32,071 — a $10,071 difference.
How often should interest compound?+
More frequent compounding means slightly more growth. Daily compounding is marginally better than monthly for savers. However, the difference is small — going from annual to monthly compounding at 7% for 20 years on $10,000 adds about $425.
What does the Rule of 72 mean?+
The Rule of 72 estimates how long it takes to double an investment: divide 72 by the annual return rate. At 6%, money doubles every 12 years. At 9%, every 8 years. It works for any compound growth rate.
What is the effective annual rate (EAR)?+
The effective annual rate accounts for compounding within a year. If the nominal rate is 6% compounded monthly, the EAR is (1 + 0.06/12)^12 − 1 = 6.17%. This is the true annualized return.