What math does the compound interest calculator use?
The annual return is divided by 12 to get a monthly rate. The initial deposit grows by that rate every month for the full number of months. Separately, each monthly contribution grows from the month it is added until the end.
Rather than adding up hundreds of individual deposits, the calculator uses the future value of an annuity, a formula that totals a stream of equal payments and all their compounding at once. The worked example on this page assumes each contribution lands at the end of the month.
Total contributions are simply the initial deposit plus the monthly amount times the number of months. Subtracting that from the future balance leaves total interest earned, the part of the balance that came from growth rather than from you.
FV = P × (1 + i)^N + C × ((1 + i)^N − 1) ÷ i i = annual return ÷ 12, N = years × 12
- FV
- future balance
- P
- initial deposit
- C
- monthly contribution
- i
- monthly rate
- N
- number of months
Example: $5,000 to start and $250 a month for 15 years
Scenario: Jordan opens a savings plan with $5,000 and sets up an automatic $250 transfer every month. Jordan assumes an illustrative 5% annual return compounded monthly for 15 years, with deposits at the end of each month.
- Monthly rate and months5% ÷ 12 = 0.4167% (0.0041667); 15 × 12 = 180 months
- Growth factor(1.0041667)^180 = 2.113704
- Initial deposit grows to$5,000 × 2.113704 = $10,568.52
- Monthly deposits grow to$250 × (2.113704 − 1) ÷ (0.05 ÷ 12) = $66,822.24
- Future balance$10,568.52 + $66,822.24 = $77,390.76
- Contributions vs interest$5,000 + $250 × 180 = $50,000 contributed; $77,390.76 − $50,000 = $27,390.76 interest
Jordan's plan would reach about $77,390.76, of which $27,390.76 is interest.
If deposits were made at the start of each month instead, each would earn one extra month of interest and the balance would be slightly higher.
What can you plan with a compound interest calculator?
Setting an automatic transfer amount
Try $100, $250 and $500 a month and compare the ending balances. Seeing the result in dollars helps you pick an amount that is meaningful without straining your budget.
Seeing the payoff of starting with a lump sum
Change only the initial deposit to see what a tax refund or bonus adds over the full period. Because it compounds the longest, a lump sum early can matter more than its size suggests.
Comparing savings vehicles
Run the same plan at the rate a savings account pays and at a lower and higher return. The spread shows how much the choice of where the money sits affects the outcome.
Finding when growth takes over
Increase the years until total interest earned passes total contributions. That crossover point is a concrete way to see compounding at work.
Which assumptions trip people up?
Using an optimistic return for safe savings
A savings account or CD pays its stated rate, not a stock market average. If the money will sit in an insured account, use a rate close to what that account pays.
Reading future dollars as today's dollars
A balance 30 years out will buy much less than the same number today. Subtract an assumed inflation rate from the return, or use the savings, taxes and inflation calculator, for a truer picture.
Ignoring tax on interest
Interest in an ordinary savings account is taxable each year, which trims the amount left to compound. The projection here is before tax.
Assuming contributions never change
In practice deposits often rise with income, or pause during tight months. Rerun the calculator when your contribution changes rather than relying on a single projection.
How does the split between contributions and interest change with time?
In the early years almost all of the balance is your own money; in later years interest dominates. On Jordan's plan, interest is about 15% of the balance after five years but nearly 59% after 30 years.
Notice that doubling the time from 15 to 30 years nearly triples the balance, while contributions do not quite double. That gap is the compounding that later years add on top of earlier growth.
| Years | Future balance | Total contributions | Interest earned |
|---|---|---|---|
| 5 | $23,418.31 | $20,000.00 | $3,418.31 |
| 10 | $47,055.62 | $35,000.00 | $12,055.62 |
| 15 | $77,390.76 | $50,000.00 | $27,390.76 |
| 20 | $116,321.62 | $65,000.00 | $51,321.62 |
| 30 | $230,403.38 | $95,000.00 | $135,403.38 |
Terms used on this page
- Compound Interest
- Compound interest is interest earned or charged on both the original principal and the interest that has already built up. Each period's interest is added to the balance, so the next period's interest is a little larger. Over long stretches, compounding makes savings grow faster and unpaid debts grow faster too.
- APY (Annual Percentage Yield)
- APY is the amount you actually earn on savings in one year, expressed as a percentage, after accounting for how often interest compounds. A higher compounding frequency pushes APY above the stated interest rate. Banks must disclose APY under federal Truth in Savings rules, so it is the fairest way to compare accounts.
- Principal
- Principal is the amount of money you borrow, or the amount you deposit, before any interest. On a loan, it is the balance that interest is charged against, and each payment's non-interest portion reduces it. On savings, principal is your own money, the base on which interest is earned.
- Inflation
- Inflation is the general rise in prices over time, which reduces how much a dollar can buy. In the US it is most often measured by the Consumer Price Index, published monthly by the Bureau of Labor Statistics. When your savings earn less than inflation, their purchasing power shrinks even though the dollar balance grows.
Compound Interest Calculator: common questions
How much will I have if I save $250 a month for 15 years?
At an illustrative 5% annual return compounded monthly, $250 a month for 15 years grows to about $66,822.24 on its own, from $45,000 of deposits. Adding a $5,000 starting deposit brings the total to about $77,390.76. A lower return would give less and a higher one more, so try a few rates in the calculator above.
What is the formula for compound interest with monthly contributions?
The formula is FV = P × (1 + i)^N + C × ((1 + i)^N − 1) ÷ i, where i is the monthly rate and N the number of months. The first term grows the starting deposit; the second totals every monthly contribution with its compounding. This version assumes deposits at the end of each month.
Is it better to make a bigger first deposit or bigger monthly deposits?
Over long periods, a dollar deposited earlier always grows more than a dollar deposited later at the same return. But most people can add more over time through monthly saving than they can put in up front. The calculator lets you test both: raise the initial deposit by a set amount, then instead raise the monthly amount, and compare.
When does interest earned exceed my contributions?
It depends mainly on the return and the time. In the example on this page, at 5% with $250 a month and a $5,000 start, interest overtakes contributions after about 23 years and 9 months. At 20 years interest is $51,321.62 against $65,000 contributed; at 30 years it is $135,403.38 against $95,000. Higher returns bring the crossover sooner.
Does this compound interest calculator include taxes?
No, results are before tax. Interest from a savings account or CD is generally taxable as ordinary income in the year it is credited, which reduces the money left to compound in a taxable account. Tax-advantaged accounts can defer or avoid that drag, depending on the type. Use the savings, taxes and inflation calculator for an after-tax estimate.
What annual return should I use for a savings account?
Use the APY your account actually pays or one close to it, and remember that savings account rates can change at any time. If you are projecting many years ahead, running both a lower and a higher rate gives a more honest range than one precise-looking number. Investment returns are a different and riskier assumption.
Why does my bank statement show less interest than the calculator?
Usually because the rate, timing or compounding differs from your inputs. Banks may compound daily and credit monthly, rates on savings accounts change over time, and deposits may not land on the same day each month. Withdrawals and fees also lower the balance. The calculator assumes a fixed rate and perfectly regular deposits.
Is compound interest the same as APY?
Not exactly. Compound interest is the process of earning interest on interest. APY is a single number that measures the result over one year, including compounding. A 5% rate compounded monthly produces an APY of about 5.12%. This calculator applies the monthly rate directly, so its results already reflect that effect.
Can compound interest work against me?
Yes, the same math that grows savings grows debt. Credit card balances compound interest on unpaid interest, which is why carrying a balance gets expensive. If you carry high-rate debt while saving at a lower rate, the debt is likely compounding faster than your savings are. Paying down a balance that charges more than your savings earn is, in effect, a guaranteed return equal to that rate.
Sources
- Compound Interest Calculator — U.S. Securities and Exchange Commission (Investor.gov). Accessed October 17, 2026.
- Compound interest (glossary) — U.S. Securities and Exchange Commission (Investor.gov). Accessed October 17, 2026.
- Topic no. 403, Interest received — Internal Revenue Service. Accessed October 17, 2026.
We cite primary sources: regulators, central-bank data and federal agencies. Worked examples on this page are our own calculations, last checked October 17, 2026. See our methodology.