How to calculate compound interest
A = P(1 + r/k)^(k·t) + C × ((1 + rₘ)ⁿ − 1) ÷ rₘ rₘ = effective monthly rate, n = months For beginning-of-month contributions, multiply the contribution future value by (1 + rₘ).
Worked example. Balance after 20 years: $144,573.
Example inputs — Initial deposit: $10,000; Monthly contribution: $200; Annual interest rate: 7%; Years: 20 yrs; Compounding: Monthly; Contribution timing: End of month. Starting values are illustrative.
From George Guju, founder of Calculyn · Educational calculator guidance, not professional advice.
Common questions answered
How it works
Compound interest means you earn interest on your interest. The more often interest compounds and the longer you stay invested, the faster your balance grows. Beginning-of-month contributions earn one extra month of growth compared with end-of-month contributions.
Using the compound interest estimate
Compound interest means growth can earn additional growth. This calculator separates the starting balance, deposits and growth so you can see which part of an ending value comes from saving and which part comes from the chosen interest assumption. It works best as a comparison tool for consistent rates and planned deposits, not as a prediction of a variable investment's performance.
Step-by-step inputs
- Initial deposit. Replace the starting value with your own, keeping the displayed unit and period. Starting example: $10,000 .
- Monthly contribution. Replace the starting value with your own, keeping the displayed unit and period. Starting example: $200 .
- Annual interest rate. Replace the starting value with your own, keeping the displayed unit and period. Starting example: 7% .
- Years. Replace the starting value with your own, keeping the displayed unit and period. Starting example: 20 yrs.
Worked example with the starting values
Using the starting inputs, the estimate is Balance after 20 years: $144,573 .
- Total contributions
- $58,000
- Interest earned
- $86,573
- Effective annual rate
- 7.23%
Compare annual interest rate scenarios
All other inputs stay at their starting values. These are modeled comparisons, not quotes, predictions or individual recommendations.
| Annual interest rate | Balance after 20 years |
|---|---|
| 3% | $83,868 |
| 5% | $109,333 |
| 7% | $144,573 |
Make a useful comparison
Start with the balance already available and enter only new deposits in the contribution field. Otherwise the same money can be counted twice. Keep the deposit period consistent: a monthly amount should reflect what you can add every month, rather than an annual total.
Change one variable at a time. Compare a lower and higher rate with the same starting balance, contribution and timeline, then compare timelines with the rate fixed. That separates the effect of more saving time from the effect of optimistic return assumptions.
Compare interest rates using the compounding convention shown by the calculator. Nominal annual rates and effective annual yields are not always interchangeable. For a deposit account, use the institution's published terms and check whether the advertised yield already includes compounding.
Common mistakes to avoid
- A constant-rate projection does not capture market losses or changing bank rates. The graph's smoothness comes from the model, not from evidence about future returns.
- Taxes, account fees and inflation can reduce the value you can spend. The ending nominal balance alone does not tell you how much purchasing power you will have.
- Do not assume every contribution earns interest for the whole timeline. Later deposits have fewer periods to grow. Contribution timing can explain differences between calculators even when the annual rate and total deposits match.
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Assumptions & limitations
- A constant rate of return or inflation every year.
- Excludes fees and taxes unless entered.
- Contributions are made regularly and on time.
Formula and assumptions reviewed October 2026 by the Calculyn team. How we build our calculators
Frequently asked questions
What is the compound interest formula?
For a starting balance without deposits, A = P(1 + r/k)^(kt), where r is the annual rate as a decimal, k is compounding periods per year and t is years. This tool also adds end-of-month deposits using the effective monthly growth rate.
How do you calculate compound interest by hand?
Convert the annual rate to a decimal, divide by compounding periods, add one and raise that factor to the number of periods, then multiply by principal. Subtract principal for interest earned. Recurring deposits need a separate annuity calculation.
How long does it take for money to double? (Rule of 72)
Divide 72 by the annual percentage rate for a rough doubling time: at 8%, about 9 years. It assumes positive steady growth and no deposits; the exact time depends on compounding frequency.
What interest rate do I need to reach my savings goal?
Fix the starting amount, deposit schedule and deadline, then try rates until the projected balance reaches the target. This calculator projects a balance, not an automatically solved rate. A required return is not evidence that an investment can deliver it.
How does compounding frequency affect returns?
At the same positive nominal annual rate, more frequent compounding raises effective annual growth. This tool converts the selected frequency to an effective monthly rate for contributions; an advertised APY already includes compounding.
What is the difference between simple interest and compound interest?
Simple interest is based only on original principal; compound interest also grows on previously earned interest. For identical positive rates and no withdrawals, compounding produces a larger balance over time.
What's the difference between APR and APY?
APR is the simple yearly rate. APY (effective annual rate) includes the effect of compounding, so it's slightly higher.
Can compounding replace regular saving?
No. Contributions and time are separate inputs. At modest starting balances, regular deposits can account for a large share of the result.
Is the assumed rate guaranteed?
No. It is a scenario input. Confirm deposit terms for savings products; investment returns can vary and can be negative.