Compound interest calculator
Use this interest calculator to estimate compound interest, compare different contribution schedules, and see how an assumed rate, time period, and compounding frequency affect future value.
Estimated balance after 20 years
- Total contributed
- $77,000
- Interest earned
- $99,472
- Estimated balance after 20 years
- $176,472
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The short answer
Compound interest is interest earned on your interest. Enter a starting balance, a monthly contribution, an annual rate and a time frame, and this calculator estimates the future value. The longer the money compounds and the more often it compounds, the larger the gap between what you put in and what you end with.
How compound interest works
With simple interest you earn a return on your original deposit only. With compound interest, each period's return is added to the balance, so the next period earns a return on a bigger number.
A worked example
Start with $5,000, add $300 a month, assume a 7% annual return compounded monthly, and run it for 20 years. You contribute $77,000 in total.
What the estimate does not include
Inflation — a nominal 7% return is not 7% of purchasing power.
Tax on interest, dividends or gains held outside a tax-advantaged account.
Fund fees and platform charges, which come straight off the return.
Sequence of returns: real markets do not deliver a flat percentage every year.
How compound interest grows your money over time
Compound interest means you earn returns on your initial principal and on all accumulated interest from previous periods. Unlike simple interest, which calculates returns only on your starting balance, compound interest accelerates growth because your earnings generate their own earnings.
Principal: the initial amount you deposit or invest before any interest accrues.
Interest rate: the annual percentage the account pays, expressed as a decimal in formulas.
Compounding frequency: how often interest gets calculated and added to your principal balance.
Time horizon: the total number of years you allow your money to grow undisturbed.
The compound interest formula and calculation mechanics
The standard compound interest formula is A = P(1 + r/n)^(nt), where A represents the future value, P is principal, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is time in years. This future value calculator formula handles any compounding frequency.
Daily compounding applies the formula 365 times per year, maximizing growth for any given rate.
Annual compounding multiplies principal by (1 + r) once per year, the simplest calculation method.
Continuous compounding uses the formula A = Pe^(rt), representing the theoretical maximum growth rate.
Interest computation differences: daily compounding on $10,000 at 5% yields $28 more than annual after one year.
Using the Rule of 72 for quick mental estimates
The Rule of 72 offers a shortcut to estimate how long it takes to double your money. Divide 72 by your annual interest rate (as a whole number, not decimal) to get the approximate number of years.
Rule of 72 accuracy: at 8% interest, it estimates 9 years; actual doubling takes 9.01 years.
For rates below 3%, use Rule of 70; for rates above 12%, use Rule of 69.
Quadrupling time: divide 144 by the interest rate to estimate when your money grows fourfold.
Tripling time: divide 115 by the rate to estimate when your balance reaches three times principal.
APY versus APR: understanding what banks advertise
Banks advertise Annual Percentage Yield (APY) for deposit accounts and Annual Percentage Rate (APR) for loans. What is APY?
APY formula: (1 + r/n)^n - 1, where r is APR and n is compounding frequency.
A 4% APR compounded quarterly yields 4.06% APY; daily compounding yields 4.08% APY.
Certificate of deposit disclosures must show APY to allow direct comparison across different term lengths.
Credit cards quote APR because compounding works against you, minimizing the apparent cost of borrowing.
Practical scenarios: retirement accounts and emergency funds
Apply compound interest principles to retirement planning. Contributing $500 monthly to a tax-deferred account earning an average 7% annual return results in $609,000 after 30 years—$429,000 coming from compound growth on your $180,000 in contributions.
Maxing a Roth IRA at $7,000 annually for 30 years at 6% yields $587,000 total.
Contributing $200 monthly from age 25 to 35, then stopping, beats contributing $200 monthly from 35 to 65.
Three-month emergency fund of $12,000 in 4% account earns $40 monthly in compound interest.
Compounding frequency matters more on larger balances: $100,000 shows $50 annual difference between daily and monthly.
The formula
FV = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)] — P = starting balance, r = annual rate, n = compounds per year, t = years, PMT = contribution per period.
FAQ
How the interest calculator estimates compound growth
Compound interest applies each period’s rate to the starting balance plus previously credited interest. This interest computation differs from simple interest, which calculates interest only on the original principal. A daily compound interest calculator uses more compounding periods than a monthly or annual model, although the practical difference depends on the stated rate, account terms, and length of time.
Enter a starting amount, recurring contribution, assumed return, compounding frequency, and time horizon. The resulting future value calculator estimate is not a guarantee, particularly when modeling an investment with changing returns. For deposit accounts such as high yield savings, compare the annual percentage yield rather than relying only on the stated interest rate. The rule of 72 can provide a rough mental estimate, but a calculator offers more detail.
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