How it's calculated
Let P = initial investment, r = annual rate, n = compounding periods per year, t = years and M = monthly contribution. Then the rate per period is i = r/n, there are N = n·t periods, and each period receives c = M·12/n of contributions.
FV = P·(1 + i)^N + c·[(1 + i)^N − 1] / i (contributions at the end of each period)
FV = P·(1 + i)^N + c·[(1 + i)^N − 1] / i · (1 + i) (contributions at the start of each period)
If i = 0: FV = P + c·N
The calculator actually steps through every period (B = B·(1+i) + c for end-of-period, B = (B + c)·(1+i) for start-of-period) so it can build the year-by-year table and handle withdrawals; our tests confirm the step-by-step result equals the closed-form formula above to within one part in a billion.
Assumptions, stated plainly
- Constant rate. The same annual rate every year. Real investments go up and down; use this to understand the math, not to predict returns.
- Contributions are pooled per compounding period. With monthly compounding you deposit M each month. With quarterly compounding, three months of deposits (3·M) are added once per quarter; with annual compounding, 12·M is added once per year; with daily compounding, M·12/365 is added each day. This is the same convention the SEC's investor.gov calculator uses (see the comparison below). It means annual compounding with "end of period" timing is conservative: a January deposit earns nothing until the year ends.
- Inflation. "Today's dollars" = nominal balance ÷ (1 + inflation)years. Inflation does not change the nominal balance.
- Withdrawals are fixed nominal amounts (they do not rise with inflation), pooled per period like contributions, and stop when the balance reaches $0.
- No taxes, fees or contribution limits are applied. Whole years only (0–100).
Cross-check against the SEC's investor.gov calculator
The U.S. Securities and Exchange Commission publishes a compound interest calculator on investor.gov. Its page describes the monthly contribution as an amount "you plan to add to the principal every month" and lets you pick annual to daily compounding. On 2026-10-17 we ran the scenarios below through investor.gov and compared its final values with this calculator (contributions at the end of each period). The results were identical to the cent, which also confirmed investor.gov's convention: it adds 12 × monthly ÷ n at the end of each compounding period.
| # | Inputs | investor.gov | InvestorMath | Difference |
|---|---|---|---|---|
| A | $10,000.00 start + $0.00/mo, 10 yrs, 5%, compounded annually | $16,288.95 | $16,288.95 | $0.00 ✓ |
| B | $5,000.00 start + $100.00/mo, 20 yrs, 7%, compounded monthly | $72,286.36 | $72,286.36 | $0.00 ✓ |
| C | $1,000.00 start + $200.00/mo, 30 yrs, 6%, compounded annually | $195,483.14 | $195,483.14 | $0.00 ✓ |
| D | $0.00 start + $500.00/mo, 10 yrs, 8%, compounded quarterly | $90,602.97 | $90,602.97 | $0.00 ✓ |
| E | $25,000.00 start + $250.00/mo, 15 yrs, 4.5%, compounded daily | $113,362.20 | $113,362.20 | $0.00 ✓ |
| F | $10,000.00 start + $100.00/mo, 5 yrs, 0%, compounded monthly | $16,000.00 | $16,000.00 | $0.00 ✓ |
| G | $2,000.00 start + $50.00/mo, 25 yrs, 10%, compounded semiannually | $85,739.20 | $85,739.20 | $0.00 ✓ |
Worked examples
1. A lump sum with annual compounding
$10,000 at 5% compounded once a year for 10 years, no contributions: FV = 10,000 × 1.0510 = 10,000 × 1.628895 = $16,288.95. Interest earned: $6,288.95. Load this example
2. Monthly contributions with monthly compounding
$5,000 to start plus $100 at the end of every month for 20 years at 7%, compounded monthly. Here i = 0.07/12 = 0.005833, N = 240 and (1 + i)240 = 4.038739.
Initial investment: 5,000 × 4.038739 = $20,193.69. Contributions: 100 × (4.038739 − 1) ÷ 0.005833 = $52,092.67. Total: $72,286.36, of which $29,000.00 is money you put in and $43,286.36 is interest. investor.gov gives the same $72,286.36 (scenario B above). Load this example
3. Save, then withdraw, with inflation
$500 a month for 30 years at 7% (monthly compounding) grows to $609,985.50. With 2.5% inflation that is about $290,806.12 in today's dollars. Withdrawing $4,000 a month for the next 25 years (still earning 7%) leaves $252,135.30 at the end. Withdrawing $5,000 a month instead runs out in year 48, about 18 years into withdrawals. Remember these withdrawals are fixed in dollars; with 2.5% inflation, $4,000 buys less every year (the "today's dollars" column shows the effect). Load this example
Frequently asked questions
How do I calculate compound interest with monthly contributions?
Add the growth of your starting amount, P(1 + r/12)^(12t), to the future value of the monthly deposits, M[(1 + r/12)^(12t) − 1]/(r/12). That is exactly what this calculator does when compounding is monthly and contributions are at the end of each month. Example 2 above walks through the numbers.
Is there a compound interest calculator with monthly contributions and inflation?
Yes, this one. Enter an inflation rate and the results show your balance in today's dollars: the nominal balance divided by (1 + inflation)^years. The year-by-year table and chart show both nominal and inflation-adjusted values.
Should I choose start or end of period for contributions?
If you invest on payday at the start of the month, "start" is closer to reality: each deposit earns interest for that month. "End" is the more common textbook and investor.gov convention and gives slightly lower results. The difference equals one period of interest on every deposit.
Why does my result differ from another compound interest calculator?
Usually because of conventions: how often interest compounds, whether deposits are at the start or end of a period, and how monthly deposits are handled when compounding is not monthly. This calculator documents its conventions above and matches the SEC's investor.gov calculator to the cent in every scenario we tested.
Does daily compounding make a big difference?
Less than most people expect. $1,000 at 5% for one year grows to $1,050.00 compounded annually, $1,051.16 monthly and $1,051.27 daily. The rate you earn and how long you invest matter far more than the compounding frequency.
What interest rate should I use?
We can't tell you what an investment will return, and no calculator can. Savings accounts and bonds state a rate; stock returns vary a lot from year to year. Many people try several rates (for example 4%, 6% and 8%) to see a range of outcomes rather than relying on one number.