Compound Interest Calculator
A = P(1 + r/n)^(nt)
How Compound Interest Works
Compound interest is interest calculated on both the original principal and the accumulated interest from previous periods. Unlike simple interest, which applies only to the principal, compounding causes your money to grow exponentially over time. Albert Einstein reportedly called compound interest the eighth wonder of the world — and the math backs up the hype.
The 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 compounding frequency per year, and t is time in years. For $1,000 at 5% compounded annually for 10 years: A = 1000 × (1.05)^10 = $1,628.89 — earning $628.89 in interest compared to $500 with simple interest.
Compounding frequency matters. Interest compounded monthly grows faster than annually because each month's interest begins earning interest sooner. At 6% over 5 years, $5,000 compounded monthly grows to $6,744.25 versus $6,691.13 with annual compounding — a $53 difference that widens dramatically over longer periods and larger sums.
The Rule of 72 provides a quick estimate: divide 72 by the annual interest rate to approximate how many years it takes to double your money. At 7% return, your investment doubles in roughly 72 ÷ 7 ≈ 10.3 years. At 4%, it takes about 18 years. This rule highlights why starting early and earning even modest returns creates substantial wealth over decades.
Compound interest works for savings accounts, CDs, bonds, retirement accounts, and investment portfolios. It also works against you on credit card debt, where unpaid balances accrue interest on interest. Use this calculator to project investment growth, compare savings strategies, or understand the true long-term cost of carrying debt.
Examples
| Example | Result |
|---|---|
| $1,000 at 5% for 10 years (annual) | $1,628.89 |
| $5,000 at 6% for 5 years (monthly) | $6,744.25 |
| $2,500 at 7% for 3 years (annual) | $3,062.61 |
| $10,000 at 4% for 20 years (quarterly) | $22,167.15 |
| $500 at 8% for 15 years (annual) | $1,586.08 |
| $20,000 at 5% for 30 years (monthly) | $89,354.89 |
| $3,000 at 3% for 7 years (monthly) | $3,700.06 |
Frequently asked questions
A = P(1 + r/n)^(nt), where P is principal, r is annual rate, n is compounding periods per year, and t is years.
More frequent compounding yields slightly higher returns. Monthly compounding is common for savings accounts; investments may compound daily.
Divide 72 by the annual interest rate to estimate years to double your money. At 6%, money doubles in about 12 years.