What a stream of equal payments grows into
An annuity in the mathematical sense is any series of equal payments at equal intervals: a monthly saving, a pension contribution, a rent. Its future value is what the whole series is worth at the end, once every payment has earned interest for the time it was invested. This calculator gives that figure for monthly payments.
The formula
Ordinary means the payment comes at the end of each period; due means at the start. The difference is one period of interest on every payment.
Worked example: $500 a month at 6% for 20 years
- Total paid in: $120,000
- Future value: $231,020
- Interest earned: $111,020 — almost as much as the payments themselves
Ordinary against due
| Payment | Rate | Years | Ordinary (end of year) | Due (start of year) |
|---|---|---|---|---|
| $1,000 / year | 6% | 10 | $13,181 | $13,972 |
| $1,000 / year | 6% | 20 | $36,786 | $38,993 |
| $1,000 / year | 8% | 10 | $14,487 | $15,645 |
| $500 / year | 6% | 10 | $6,590 | $6,986 |
Paying at the start of the period instead of the end is worth 6% more at a 6% rate — exactly one year's interest on everything. It costs nothing but timing.
Why the last years matter most
In the twenty-year example the first ten years of payments account for $60,000 of contributions but $149,080 of the final value; the second ten years contribute the same $60,000 and add only $81,940. Early payments do the work. This is the same arithmetic that makes starting a pension at 25 rather than 35 worth more than doubling the contribution later.
Where the formula applies
Retirement contributions, education savings, sinking funds for a known future cost, and the reverse question: what a lease's stream of payments is worth to the lessor. It does not apply when payments change — a raise-linked contribution needs the growing annuity formula instead.
What this calculator leaves out
Tax on the interest, fees, inflation, and any change in the payment. The rate is a constant; real returns are not.
Related calculators
- Present value of an annuity — the same stream discounted to today
- Growing annuity — when the payment rises each year
- Compound interest calculator — a lump sum plus contributions