How to Calculate Compound Interest
What is compound interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. It is the reason investments and savings grow exponentially over time, and why debt left unpaid can grow faster than people expect.
Simple interest is calculated only on the principal. Compound interest is calculated on the principal plus all previously earned interest — meaning the interest itself earns interest.
The compound interest formula
A = P(1 + r/n)^(nt)
Where: A = the final amount (principal + interest), P = principal (starting amount), r = annual interest rate (as a decimal — divide the percentage by 100), n = number of compounding periods per year (12 for monthly, 4 for quarterly, 365 for daily), t = time in years.
The interest earned = A − P.
Worked example: savings account
You deposit $10,000 in a savings account at 5% annual interest, compounded monthly, for 10 years.
P = 10,000 | r = 0.05 | n = 12 | t = 10
A = 10,000 × (1 + 0.05/12)^(12×10) = 10,000 × (1.004167)^120 = 10,000 × 1.6471 = $16,471
Total interest earned = $16,471 − $10,000 = $6,471. Without compounding (simple interest), you would have earned only $5,000.
How compounding frequency affects results
The more frequently interest compounds, the more you earn. For the same $10,000 at 5% for 10 years:
Annually (n=1): $16,289. Quarterly (n=4): $16,436. Monthly (n=12): $16,471. Daily (n=365): $16,487.
The difference between monthly and daily compounding is small ($16 on a $10,000 investment over 10 years). Annual vs. daily makes a more meaningful difference. For savings accounts and investments, monthly compounding is most common.
The Rule of 72
A useful shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6%, money doubles in approximately 72 ÷ 6 = 12 years. At 9%, approximately 8 years. This works because of the nature of exponential growth and is accurate within a few percent for rates between 2% and 15%.
Calculate compound interest
Use CalculatePilot's free compound interest calculator to compute the exact amount for any principal, rate, compounding frequency, and time period. The formula used is shown on the page. No signup required.