Compound Interest Calculator

Compound interest turns time into a visible number: a starting balance grows, each period’s interest is added back to the balance, and any steady contributions join the same compounding schedule. This calculator estimates that process from five inputs: starting amount, annual interest rate, years, monthly contribution, and compounding frequency. The result separates the future value from the amount you personally contributed, so you can see how much of the ending balance came from deposits and how much came from interest.

Use this page for savings plans, investment illustrations, certificate of deposit comparisons, and educational scenarios where the return is treated as steady. It is especially helpful when you want to test tradeoffs. A slightly higher monthly contribution, a longer time horizon, or a different compounding frequency can change the future balance without changing the starting amount. For a one-time lump sum without contributions, use the future value calculator. For a fixed target and monthly saving plan, compare with the savings goal calculator. If interest does not compound at all, the simple interest calculator is the cleaner model.

What the calculator actually computes

The form accepts a starting amount, a nominal annual rate, a number of years, an optional monthly contribution, and a compounding frequency such as annually, quarterly, monthly, or daily. In the calculator, the annual rate is divided by the compounding frequency to get a periodic rate. The number of years is multiplied by that frequency to get the number of compounding periods.

The contribution handling is important. The form label says monthly contribution, but the calculation converts that amount into the selected compounding period by multiplying by 12 and dividing by the frequency. With monthly compounding, $200 per month remains $200 per period. With quarterly compounding, the same entry becomes $600 per quarter. With daily compounding, it is spread into a small daily equivalent. The calculator then treats those deposits like an ordinary annuity added at the end of each compounding period.

Formula

For the starting balance alone, compound interest uses:

$FV_{\text{principal}} = PV \times \left(1 + \frac{r}{m}\right)^{m \times t}$

For the converted periodic contributions, the calculator adds:

$FV_{\text{contributions}} = PMT \times \frac{\left(1 + \frac{r}{m}\right)^{m \times t} - 1}{\frac{r}{m}}$

The full result is:

$FV = FV_{\text{principal}} + FV_{\text{contributions}}$

where:

• $PV$ is the starting amount;
• $r$ is the annual interest rate as a decimal;
• $m$ is the number of compounding periods per year;
• $t$ is the number of years;
• $PMT$ is the contribution converted into one compounding period; and
• $FV$ is the future value.

When the rate is zero, the contribution portion is simply the periodic contribution multiplied by the number of periods, because there is no interest factor to apply.

Example: calculating compound interest

Suppose the starting amount is $10,000, the annual interest rate is 7%, the time is 10 years, the monthly contribution is $200, and compounding is monthly. The periodic rate is 0.07 divided by 12, or about 0.005833. The number of periods is 12 multiplied by 10, or 120. The growth factor is about 2.009661.

The original $10,000 grows to about $20,096.61:

$10{,}000 \times \left(1 + \frac{0.07}{12}\right)^{120} = 20{,}096.61$

The contribution is $200 per monthly period, so the contribution stream grows to about $34,616.96:

$200 \times \frac{\left(1 + \frac{0.07}{12}\right)^{120} - 1}{\frac{0.07}{12}} = 34{,}616.96$

Add those pieces and the result is a future value of about $54,713.58. Total contributed equals the $10,000 starting amount plus $24,000 of monthly deposits, or $34,000. Interest earned is therefore about $20,713.58. That is the number shown in the detail rows as the growth produced by compounding rather than by your own deposits.

Compound interest versus related TVM tools

Compound interest is part of the time value of money family, but each calculator answers a different question. The present value calculator discounts a future lump sum backward to today. The future value calculator grows one current lump sum forward. The Rule of 72 calculator estimates how long a steady compound rate takes to double. The CAGR calculator solves for the single annual rate that links a beginning value to an ending value.

The compound interest calculator is broader than a single-sum future value calculation because it includes contributions. It is also more detailed than the Rule of 72 because it returns dollars rather than a rough doubling time. That makes it suitable for questions such as, “What could this savings plan become?” or “How much of the ending balance is deposits versus interest?”

Practical tips

• Match the compounding frequency to the rate source. If an account says interest compounds daily, choose daily.
• Keep the rate realistic. A high expected return can make the model look precise while hiding risk.
• Compare scenarios one input at a time so you know which lever changed the result.
• Remember that contributions are assumed steady and converted into the compounding period.
• Use nominal dollars unless you separately adjust the rate for inflation.
• Treat the estimate as informational, not investment advice. Tax rules, fees, risk tolerance, and market volatility can all change a real plan.

Sources

• Regulation DD Appendix A—Annual Percentage Yield Calculation — eCFR current through 2026-07-09; Authoritative periodic-interest/APY assumptions; algebraic future-value, inverse-rate, and continuous-growth extensions remain disclosed publisher mathematics.
• Calculation scope: The equations and assumptions described above are applied only to values entered in the form. No live rates, prices, tax rules, lender terms, or accounting classifications are fetched. Results are user scenarios, not quotes or prescribed classifications.