How compound interest is calculated
FV = P × (1 + r/n)^(n × t) + PMT × ((1 + i)^(12 × t) − 1) / i i = (1 + r/n)^(n/12) − 1
P is the starting amount, r the annual interest rate as a decimal, n the number of times interest compounds per year (1, 4, 12 or 365), t the number of years and PMT the monthly contribution. The first half of the formula is the classic compound interest formula for a single deposit; the second half adds up every monthly contribution together with the interest it earns until the end.
Contributions are monthly, but interest may compound yearly, quarterly or daily. To combine the two, the calculator converts the annual rate into its equivalent monthly rate i — the monthly rate that grows money exactly as much over a year as n periods at r/n. Each contribution is assumed to arrive at the end of its month. With monthly compounding, i is simply r/12.
The effective annual rate, (1 + r/n)^n − 1, shows what the compounding frequency adds. At 12% a year it is 12.55% with quarterly, 12.68% with monthly and 12.75% with daily compounding.
Worked example
Say you start with $10,000, add $200 at the end of every month and earn 5% a year, compounded monthly, for 20 years. You pay in $58,000 in total: the $10,000 you start with plus 240 contributions of $200.
The balance grows to $109,333.14, of which $51,333.14 — 47% — is interest. In the first year the balance earns $567.39 in interest; in year 20 it earns $5,257.68.
With inflation at 3% a year, $109,333.14 in 20 years will buy roughly what $60,535.11 buys today.
How to read the results
Final balance is what the account would hold at the end. Total paid in is everything you contributed, including the starting amount, and total interest is the difference: the part compounding produced.
The value in today's money deflates the final balance by the inflation rate you entered, for every year of the period. If the interest rate is below inflation, the real value can end up below what you paid in even though the balance keeps rising.
The chart and the table show how growth speeds up: early on, almost all of the balance is your own money; later, interest earned on earlier interest does more and more of the work. That is why starting early usually matters more than squeezing out a slightly higher rate.
Assumptions and limits
- The interest rate stays the same for the whole period.
- Contributions are made at the end of every month and never change.
- No taxes, fees or withdrawals are deducted. Tax on interest, such as a withholding tax, lowers the real result.
- Inflation is a constant rate you choose; actual inflation varies from year to year.
- Results are estimates for planning, not an offer or investment advice.
Frequently asked questions
What is the formula for compound interest?
For a single deposit, FV = P × (1 + r/n)^(n × t), where P is the starting amount, r the annual rate, n the number of compounding periods per year and t the number of years. For example, 10,000 at 5% compounded monthly for 10 years grows to about 16,470.
How much difference does the compounding frequency make?
Less than most people expect. More frequent compounding adds a little, because interest starts earning interest sooner: 12% a year becomes an effective 12.55% with quarterly, 12.68% with monthly and 12.75% with daily compounding. The rate itself and how long you stay invested matter far more.
What is the difference between simple and compound interest?
Simple interest is paid only on the original amount: 1,000 at 10% earns 100 a year, or 1,000 over ten years. With yearly compounding the interest is added to the balance, so the same 1,000 grows to 2,593.74 in ten years — 1,593.74 of interest.
How long does it take to double my money?
A quick estimate is the rule of 72: divide 72 by the annual rate. At 6% money doubles in about 12 years, at 12% in about 6. The exact time with yearly compounding is ln(2) ÷ ln(1 + r), which is 11.9 years at 6%.
Why does inflation matter for compound interest?
Because a balance in the future buys less than the same amount today. If your money earns 5% while prices rise 3% a year, your purchasing power grows by only about 1.9% a year: (1.05 ÷ 1.03) − 1. Enter an inflation rate to see the result in today's money.