Compound Interest Calculator

The formula, split into principal and contributions

The future value is the sum of two parts. The starting amount grows by the compound interest formula P × (1 + r/n)^(n×t), where r is the annual rate as a decimal, n the number of compounding periods per year and t the number of years. The contributions grow by the ordinary annuity formula C × ((1 + r/n)^(n×t) − 1) ÷ (r/n), with each deposit assumed to arrive at the end of a period.

Because the contribution box is monthly but compounding can be annual, quarterly or daily, the tool converts your monthly figure into one deposit per compounding period: C = monthly contribution × 12 ÷ n. At monthly compounding that is just the number you typed; at quarterly it becomes 600 for a 200 monthly contribution, and at daily it becomes 6.58.

Worked through with the defaults (10,000 start, 200 a month, 7%, 20 years, monthly): the period rate is 0.07 ÷ 12 = 0.0058333 and there are 240 periods, giving a growth factor of 4.0387. The principal becomes 10,000 × 4.0387 = 40,387.39, the contributions become 200 × (4.0387 − 1) ÷ 0.0058333 = 104,185.33, and the future value is 144,572.72. Total invested is 10,000 + 200 × 12 × 20 = 58,000, so Total interest is 86,572.72.

What each frequency button does to the default inputs

The gap between Annually and the other options is larger than compounding alone would explain. Under annual compounding the whole year of contributions is treated as one 2,400 deposit at the end of the year, so that money earns nothing until the following year. Under daily compounding the deposits are spread across the year and start earning almost immediately. Pick the frequency that matches how your account actually credits interest.

Time matters more than the rate

Leaving the other defaults alone and changing only the years shows why starting early is the advice everyone gives. After 10 years the balance is 54,713.58 on 34,000 invested; after 20 it is 144,572.72 on 58,000; after 30 it is 325,159.17 on 82,000. The last decade adds more than the first two combined, even though the deposits are identical.

The rule of 72 is a quick sanity check against the tool: money doubles roughly every 72 ÷ rate years, so about 10.3 years at 7%. Set the contribution to 0 and 10 years and the growth factor comes out at 2.01, which matches.

Assumptions baked into the result

• The rate is fixed for the entire period. Real returns on investments vary year to year, so treat the output as a projection at an average rate, not a forecast.
• No tax, fees or withdrawals are deducted. For an account that charges an annual fee, subtract it from the rate before entering it.
• Inflation is ignored. To see growth in today's money, enter the rate minus expected inflation: 7% nominal with 3% inflation becomes roughly 4%.
• Contributions are constant for the whole term. If you expect to increase them, run the tool in stages and carry each future value forward as the next starting amount.
• A rate of 0 works: the future value is then just the starting amount plus every contribution, which is 58,000 on the defaults.

Questions the three results can answer

• How much do I need to save each month to reach a target? Adjust the monthly contribution until Future value reaches the goal.
• Is a lump sum or a monthly plan better? Compare a one-off starting amount with 0 contributions against 0 start with the same total spread monthly.
• What is the interest really worth? Total interest is the part of the balance you did not deposit yourself, which is the clearest measure of what compounding added.