The Concept
What is the future value of an annuity?
An annuity is simply a series of equal payments made at regular intervals — a monthly deposit into an investment account, an annual pension contribution, or any fixed, repeating payment. Its future value is what that whole stream of payments grows into once each one has earned compound interest up to the end of the term. Early payments compound the longest and do the most work, which is why the total ends up far larger than the sum of the payments themselves.
This calculator is built for the payment stream itself, with no opening lump sum, so you can see exactly what your contributions alone produce. If you also want to start from an existing balance, the future value calculator adds a lump sum on top of the payments, and the future value with monthly contributions guide explains the mechanics.
The Two Types
Ordinary annuity vs annuity due
Annuities come in two timings, and this calculator handles both with the toggle at the top:
- Ordinary annuity — each payment lands at the end of the period. This is the default and the most common case for things like loan-style contributions.
- Annuity due — each payment lands at the beginning of the period, so every payment compounds for one extra period and the total is slightly higher.
The difference is real but small. The same $500 a month over 20 years at 7 percent reaches about $260,463 as an ordinary annuity and about $261,983 as an annuity due — roughly $1,500 more for paying at the start of each month rather than the end.
Which timing does your situation actually use?
Guessing wrong only moves the answer by a fraction of a percent, but it is easy to get right. End-of-period payments are the default across personal finance, which is why the ordinary annuity is the standard case:
- Bond interest. Coupons are paid at the end of each period, so a bond's income stream is a textbook ordinary annuity.
- Investing out of a paycheck. If you transfer money after being paid at month-end, the contribution lands at the close of the period.
- Loan and mortgage payments. Amortised loans are built on end-of-period math — the same structure seen from the borrower's side.
- Rent, leases and insurance premiums. These are usually paid in advance, at the start of the period, which makes them annuities due.
The rule of thumb: if the money moves before you receive the thing you are paying for, it is an annuity due; if it moves after, it is an ordinary annuity.
How To
How to use this calculator
Set the timing, then fill in four inputs:
- Payment timing — ordinary (end of period) or annuity due (beginning of period).
- Payment amount — the fixed sum you contribute each period.
- Annual interest rate — the yearly rate of return you expect.
- Number of years — how long you keep contributing.
- Payment frequency — monthly, quarterly or annually. Payments compound at the same frequency.
The result splits the future value into what you paid in and the interest earned on top, and the year-by-year breakdown shows the balance building period after period.
The Formula
The future value of an annuity formula
For an ordinary annuity, the future value is:
FV = PMT × [ ((1 + i)n − 1) ÷ i ]
where PMT is the payment per period, i is the periodic interest rate (the annual rate divided by the number of periods per year), and n is the total number of payments. For an annuity due, every payment is invested one period earlier, so you multiply the whole thing by one more period of growth:
FVdue = FVordinary × (1 + i)
The bracketed term is the annuity factor — it bundles every payment's individual growth into a single multiplier. The future value formula guide covers the single-sum version this builds on.
Example
Example: $500 a month
Here is how $500 a month grows as an ordinary annuity at 7 percent, compounded monthly, over different terms. Notice how the interest portion overtakes the payments as the term lengthens.
| Term | Future value | Paid in | Interest earned |
|---|
| 10 years | $86,542 | $60,000 | $26,542 |
| 20 years | $260,463 | $120,000 | $140,463 |
| 30 years | $609,985 | $180,000 | $429,985 |
Over 30 years, the $180,000 you pay in turns into about $609,985 — more than two-thirds of the final balance is interest. Switching the same 20-year plan to annuity-due timing lifts the result from $260,463 to about $261,983.
Frequency
How payment frequency affects the result
Contributing the same amount per year but more often gives each dollar more time invested. Here is $6,000 a year over 20 years at 7 percent, paid at three different frequencies as an ordinary annuity:
| Frequency | Payment | Future value |
|---|
| Annually | $6,000 / year | $245,973 |
| Quarterly | $1,500 / quarter | $257,691 |
| Monthly | $500 / month | $260,463 |
Same money in, but monthly payments finish about $14,000 ahead of annual ones — purely from starting to compound sooner each year.