APR Desk
APR Desk · Compound interest

Compound interest calculator

Future value with optional end-of-period contributions

A compound interest calculator grows a balance by applying the rate to the new total, not only to the original amount. You can also add the same contribution at the end of every compounding period. The result is a future value, the amount you put in, and the interest that makes up the difference. It is a savings and growth estimate, not a loan payment.

Inputs

Result

Enter a starting amount, a rate, and a time.

Disclaimer: An estimate of compound growth. It is not an investment forecast, a savings-account quote, or tax advice. Rates you type are nominal annual rates.

A single percent of a number, without years of compounding, is the ClearQuip percentage calculator.

How to use

  1. Enter the starting amount. Zero is allowed if you will grow the balance from contributions alone.
  2. Enter the nominal annual rate and how many years the money stays in.
  3. Choose how often the rate compounds. The contribution, if any, is added at the end of each of those periods, not on a different schedule.
  4. Press Calculate. Interest earned is the future value minus everything you put in.

How it's calculated

r = annual rate ÷ periods per year
n = years × periods per year
Future value = P × (1 + r)^n + contribution × ((1 + r)^n − 1) ÷ r

The first term grows the starting amount. The second term is the future value of an ordinary annuity: each contribution earns interest for the periods that remain after it is deposited, and the last contribution earns nothing because it arrives at the end. If the rate is zero, the future value is the starting amount plus contributions times the number of periods.

A loan payment is the reverse problem. You are paying a balance down, not growing one. Use the loan payoff calculator or the mortgage payment calculator for that. Turning a nominal APR into an effective annual yield is the APR to APY converter.

Worked example

One thousand dollars at 5 percent, compounded monthly, for 10 years and with no contribution: r = 0.05 ÷ 12 and n = 120. The future value is 1,000 × (1 + 0.05 ÷ 12)^120 = $1,647.01. The interest is $647.01. Add a contribution and both the future value and the “you put in” line rise.

Assumptions and sources

The formula is the standard compound-interest future value plus the ordinary-annuity future value, as used in introductory finance. Daily compounding uses 365 periods, not 365.25, and it does not skip weekends. Contributions are end-of-period. A contribution at the beginning of the period would earn one extra period of interest; this page does not do that. Taxes and fees are not subtracted.

FAQ

What is the difference between compound and simple interest?

Simple interest pays the rate only on the original amount. Compound interest pays the rate on the original amount plus interest already earned. This page is the compound version.

When is the contribution deposited?

At the end of each compounding period. If you compound monthly, the contribution is monthly. The form does not support a monthly deposit with yearly compounding.

Why does daily compounding not match my bank to the cent?

Banks set their own day count, posting rules, and balance method. This uses 365 equal periods and the rate you typed.

Can the starting amount be zero?

Yes, if the contribution is greater than zero. The balance then comes only from the deposits and the interest on them.

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