The formula, and the one extra term that separates due from ordinary
PMT is the deposit each period, i is the rate per period, and n is the number of periods. The bracketed part is the accumulation factor: it sums each deposit plus the compound interest it earns before the end. If the rate is 0, the formula collapses to FV = PMT × n, just the deposits added up.
Paying at the start of each period beats paying at the end
Same deposit, same rate, same number of periods. An annuity due just pays at the start of each period instead of the end, so every payment collects one more round of interest.
$1,000 a month for 10 years at 6% annual (0.5% monthly). Paying at the start of each month is worth an extra $819 here, purely from timing.
What $500 a month grows into (ordinary, 7% annual)
| Years | Total deposited | Future value | Interest earned |
|---|---|---|---|
| 10 years | $60,000 | $86,542 | $26,542 |
| 20 years | $120,000 | $260,463 | $140,463 |
| 30 years | $180,000 | $609,985 | $429,985 |
| 40 years | $240,000 | $1,312,407 | $1,072,407 |
$500 a month, 7% annual rate compounded monthly. Notice interest overtakes deposits somewhere in the twenties: at 40 years, four-fifths of the balance is growth, not what you put in.
Where the number goes wrong
- Mismatched rate and periods. Monthly deposits need a monthly rate. Feed in the annual rate and the answer is off by an order of magnitude.
- Wrong annuity type. Ordinary vs due changes the result by a factor of (1 + i). Rent and insurance premiums are usually due; loan payments are usually ordinary.
- Nominal, not real. The result ignores inflation, taxes, and fees. It is the raw balance, not its future spending power.
- Fixed everything. The formula assumes a constant deposit and a constant rate. Variable inputs need a period-by-period model instead.
Common questions
What is the difference between an ordinary annuity and an annuity due?
It is when each payment lands. An ordinary annuity pays at the end of every period; an annuity due pays at the start. Because every payment in an annuity due earns one extra period of interest, its future value is always higher, by exactly a factor of (1 + rate).
What rate and period do I use for monthly deposits?
Match the rate to the payment schedule. For monthly deposits at a 6 percent annual rate, use 0.5 percent per month (6 divided by 12) and count periods in months. Using the annual rate with monthly deposits is the most common mistake.
Does future value account for inflation?
No. The result is a nominal figure, the actual dollars in the account at the end. To see what that money will buy, divide by (1 + inflation rate) raised to the number of periods.
