Compound Interest Calculator — Growth & Contributions
Enter a starting amount, an annual rate and a number of years — with an optional monthly contribution — to see the balance grow and how much of it is interest rather than money you paid in.
Enter the details.
Contributed — · Interest earned —
Year-by-year growth
| Year | Balance | Contributed | Interest |
|---|
What this calculator does
It projects the future value of a lump sum plus a regular monthly contribution, compounding monthly at the rate you enter. The headline is the final balance, but the more useful figure is the split between the money you actually put in and the interest it earned: over long periods the interest overtakes the contributions, and the year-by-year table shows exactly when.
Method
The balance is advanced one month at a time. Each month the previous balance earns interest at the monthly rate and the contribution is added:
B ← B · (1 + r) + PMT
where r is the annual rate ÷ 100 ÷ 12 and PMT is the monthly
contribution. The closed form this reproduces is the future value of an annuity,
A = P(1+r)n + PMT·((1+r)n − 1) / r, and the year rows are the
real simulated balances, not the formula read off at each year. Setting the starting amount or the
contribution to zero shows each part on its own.
The rule of 72
A quick way to estimate doubling time: divide 72 by the annual rate. At 7% money doubles in about 72 ÷ 7 ≈ 10.3 years; at 3% it takes about 24 years. The table confirms the estimate — the balance crosses twice the contributed amount at roughly that point.
Example
| Start | Rate | Years | Monthly | Contributed | Final balance |
|---|---|---|---|---|---|
| 10,000 | 7% | 20 | 200 | 58,000 | 144,573 |
| 0 | 5% | 20 | 200 | 48,000 | 82,207 |
| 5,000 | 6.5% | 30 | 250 | 95,000 | 311,504 |
In the first row the interest, about 86,600, is larger than everything paid in — which is the point of compounding over a long horizon.
This is a projection for planning, not financial advice. It assumes a constant rate, no tax and no fees; real returns vary and can be negative.
Frequently asked questions
Is the interest rate nominal or effective?
The annual rate is applied monthly as rate ÷ 12, which is the nominal convention used by most savings and loan products. The effective annual rate is slightly higher because interest compounds: 4% nominal compounded monthly is about 4.07% effective. The year-by-year table shows the balance the nominal convention produces.
What is compound interest?
Interest that is added to the balance and then earns interest itself. A simple-interest account pays only on the original deposit; a compound account pays on the deposit plus everything already earned, so the balance grows faster the longer it is left alone. This is the whole reason starting early matters more than contributing a lot later.
How often is the interest compounded here?
Monthly. The annual rate is divided by twelve and applied to the balance each month, and contributions are added at the end of the month. Most savings accounts and investment projections quote a rate that way, though the exact compounding is set by the account and the statement governs.
What is the difference between the nominal rate and the effective rate?
The nominal rate is the quoted annual figure. Because monthly compounding earns interest on interest, the effective annual rate is slightly higher: a nominal 6% compounded monthly is about 6.17% effective. The growth table lets you see the effect rather than take it on trust.
Does this account for inflation or tax?
No. It shows the growth of the nominal balance. Inflation reduces what that balance will buy, and tax on interest reduces what you keep, so a real return is usually lower. Enter a lower rate to model either effect roughly.
Why do the contributions matter so much?
Each contribution is added early and then compounds for every remaining month. A contribution made in year one of a thirty-year projection is worth far more than the same amount made in year twenty-five, because it has had twenty-four extra years to earn interest on itself.
Go deeper
Longer explanations of the problems this tool solves:
Sources
- Compound-interest and future-value formulas for an annuity: A = P(1+r)ⁿ + PMT·((1+r)ⁿ − 1) / r, with r the monthly periodic rate and n the number of months.
- U.S. Securities and Exchange Commission, Compound Interest Calculator and investor guidance on the effect of time and fees. investor.gov
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