How to Calculate Compound Interest
Learn how to calculate compound interest using the formula A = P(1 + r/n)^(nt). Understand how frequency of compounding affects your savings or loan balance over time.
What Is Compound Interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, which only applies to the principal, compound interest causes balances to grow exponentially over time. This "interest on interest" effect makes it one of the most powerful forces in personal finance, working for you in savings accounts and against you in debt.
The Compound Interest Formula
The formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial deposit), r is the annual interest rate as a decimal, n is the number of times interest compounds per year, and t is the time in years. For example, $1,000 at 6% annual interest compounded monthly for 5 years: A = 1000(1 + 0.06/12)^(12×5) = $1,348.85. The more frequently interest compounds, the larger the final amount.
Compounding Frequencies Explained
Interest can compound annually (n=1), semi-annually (n=2), quarterly (n=4), monthly (n=12), or even daily (n=365). Daily compounding yields slightly more than monthly compounding because interest accrues more frequently. For a $10,000 deposit at 5% for 10 years, annual compounding gives $16,288.95 while daily compounding gives $16,486.65 — a difference of nearly $200.
Continuous Compounding
At the theoretical limit of infinite compounding periods, you get continuous compounding, calculated as A = Pe^(rt), where e is Euler's number (approximately 2.71828). This represents the absolute maximum growth from a given interest rate. Using the same example — $10,000 at 5% for 10 years — continuous compounding yields $16,487.21, only marginally more than daily compounding.
The Rule of 72
A quick mental shortcut to estimate doubling time is the Rule of 72: divide 72 by the annual interest rate to get the approximate number of years to double your money. At 6% interest, your money doubles in roughly 72 ÷ 6 = 12 years. At 9%, it doubles in about 8 years. This rule is most accurate for rates between 6% and 10% and assumes annual compounding.
Compound Interest on Debt
Compound interest works against you when you carry debt. Credit cards typically compound daily, meaning unpaid balances grow quickly. A $5,000 credit card balance at 20% APR compounded daily will grow to $6,107 after one year if no payments are made. Paying more than the minimum each month reduces the principal faster and significantly cuts the total interest paid.
Practical Tips for Maximizing Compound Growth
Start saving as early as possible, since time (t) has an exponential effect on the final balance. Even small additional contributions made consistently can dramatically increase your ending balance through the compounding effect. Reinvesting dividends in investment accounts is another way to harness compounding, as each dividend payment becomes new principal that itself earns returns.
Try These Calculators
Put what you learned into practice with these free calculators.
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