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Compound Interest Calculator

Grow a starting balance and a regular deposit at a chosen rate, and see how much of the result is interest.

Inputs
Compound interest resultCalculated
Balance after 20 years144,572.72
Formula
  A = P x (1 + i) ^ N        where i = r / n and N = n x t
  Deposits add PMT x ((1 + i) ^ N - 1) / i
Inputs
  P   starting principal    10,000.00
  r   annual rate           7.00%
  n   compounding periods   12 (monthly)
  t   years                 20
  PMT deposit each period   200.00

Working

i0.07 / 12 = 0.0058333333
N12 x 20 = 240 periods
(1 + i) ^ N4.038738849

Principal grows to 10,000.00 x 4.038738849 = 40,387.39

Deposits grow to 200.00 x 520.92665983104,185.33
Results
  Final balance                      144,572.72
  Total you put in                   58,000.00
  Interest earned                    86,572.72
  Growth on the original principal   30,387.39
  Value of the deposits              104,185.33
  Effective annual yield             7.2290%
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About the Compound Interest Calculator

Compounding does two jobs at once here. The starting principal grows on its own, and every deposit you add grows for however many periods remain, which is why the two halves are reported separately. Ten thousand at 7 percent compounded monthly for twenty years becomes 40,387.39 by itself, while 200 added each month becomes 104,185.33, giving a balance of 144,572.72 against 58,000 actually paid in.

Deposits are treated as arriving at the end of each compounding period, the ordinary annuity convention used by most textbooks and spreadsheets. Choosing monthly compounding therefore means a monthly deposit; choosing quarterly means the figure you type goes in four times a year. Keeping the two aligned avoids the quiet error of assuming twelve deposits while compounding only four times.

The results also show the effective annual yield, which is what the nominal rate really earns once the compounding schedule is applied. Nothing here accounts for inflation, fees or tax, all of which pull the real outcome down, so a long horizon deserves a rate you would defend in an argument rather than an optimistic one. To reverse the question and find the rate that reaches a target, use the Compound Interest Rate Calculator.

How to use

  1. Enter the starting principal, or zero if you are beginning from nothing.
  2. Set the annual rate and how often interest is compounded.
  3. Enter how much you add at the end of each compounding period, or zero for a lump sum only.
  4. Set the number of years, then compare the final balance with the total you put in.

Common questions

What is the compound interest formula?
A = P x (1 + r / n) ^ (n x t) for the principal, with deposits adding PMT x ((1 + i) ^ N - 1) / i where i is the periodic rate and N the number of periods.
When are the deposits added?
At the end of each compounding period. Depositing at the start of the period would earn slightly more, so treat this as the conservative version.
Can I model a monthly deposit with annual compounding?
Not directly. Match the compounding frequency to your deposit frequency, or convert twelve monthly deposits into one yearly figure and accept the small difference.
Does it account for inflation?
No. Subtract expected inflation from the rate before entering it if you want the answer in the purchasing power of today.