How this instrument works
In finance, an annuity is any sequence of equal payments made at equal intervals — not only the insurance contract that borrows the same word. This instrument computes the future value of that sequence: the balance sitting in the account the instant the final payment posts, with every earlier payment credited for however many periods it was actually on deposit. Payment per period, $ is what goes in each time; Rate per period, % is what that money earns each time it sits; Number of periods is how many times the payment repeats.
The formula divides by the rate because it is closed-form shorthand for adding a geometric series, not an arbitrary shape. Picture each payment as its own separate deposit: the last one, made at the very end, has not yet had a single period to grow, so it contributes only its own face value. The first one has almost the whole term of growth ahead of it. Summing (1 + r) raised to every power from 0 through n minus 1 is exactly what ((1 + r) to the n, minus 1) over r equals, and the shortcut only works because every payment and every rate stay identical from the first period to the last.
This models an ordinary annuity, where each payment lands at the end of its period — the standard shape for payroll-deducted retirement saving, sinking funds set aside for a known future cost, and level loan-style deposit plans. It assumes the rate never moves, no payment is ever skipped or late, and it ignores fees, taxes, and inflation entirely. Payments due at the start of each period instead — an annuity due — each earn one extra period of interest, raising the total by a factor of (1 + r).
- Enter the amount set aside at the end of every period into Payment per period, $.
- Set Rate per period, % to the interest rate that period actually earns — a monthly deposit needs a monthly rate, not the annual headline figure.
- Type how many payments the plan will make into Number of periods.
- Read Future value for the balance the instant the last payment lands.
- Multiply Payment per period, $ by Number of periods to see how much of that balance was actually deposited, versus what compounding added on top.
Worked example — $500 a month for ten years
Set Payment per period, $ to 500, Rate per period, % to 0.5, and Number of periods to 120 — a $500 deposit made at the end of every month, earning 0.5% each month, for ten years. Future value reads $81,939.67, computed the instant the 120th payment lands.
Multiply $500 by 120 and only $60,000 of that total was ever paid in; the other $21,939.67 is compounding — interest earned on interest, one small deposit at a time. A $1,000 monthly deposit at a 1% monthly rate for just 12 payments reaches $12,682.50, and only $682.50 of that is growth: a shorter run at double the rate still ends up with far less compounding, because Number of periods sits in the exponent and Rate per period, % does not.
Questions
Is this the same as buying an insurance annuity?
No. In finance, annuity is a general term for any sequence of equal payments at equal intervals — this instrument only does that arithmetic, showing how a stream of level deposits compounds into a future balance. Insurance companies sell a specific contract under the same name, bundling fees, mortality pricing, and a guaranteed income phase this calculation knows nothing about. Read a policy's own disclosure documents before judging one of those products.
Why does the formula divide by the interest rate?
Because dividing is the closed-form shortcut for summing a geometric series, not an arbitrary step. Each payment compounds separately: the final one, just deposited, has earned nothing yet, while the first has earned interest for nearly the whole term. Adding every one of those growth factors together equals ((1 + r) to the n, minus 1) over r exactly, which is faster than looping through n separate additions by hand.
What is the difference between this and an annuity due?
Timing. This instrument assumes an ordinary annuity, where each payment posts at the end of its period, so the last one earns zero interest before Future value is read. An annuity due assumes payments land at the start of each period instead, giving every single one an extra period to grow — multiply this result by (1 + Rate per period, %) to convert one into the other.
Does raising Number of periods matter more than raising Rate per period?
Usually, over a long run. Number of periods sits in an exponent, so it multiplies the growth factor by itself again with every step, while Rate per period, % scales it once. Ten years of $500 monthly deposits at 0.5% turns $60,000 of contributions into $81,939.67 — about 36.6% growth. A single year of $1,000 deposits at double that rate turns $12,000 into $12,682.50 — only about 5.7% growth.
How much of Future value is money I actually deposited?
Multiply Payment per period, $ by Number of periods to get that figure, then subtract it from Future value for growth alone. On the default sheet, $500 across 120 periods is $60,000 contributed against $81,939.67 total — $21,939.67 came from compounding, not from deposits. The split shifts further toward growth the longer the plan runs and the higher the rate.
What does this calculation leave out?
A constant rate, on-time payments every period, and no costs. Real accounts change their rate, real savers occasionally miss a deposit, and management fees, taxes on interest or gains, and inflation all reduce what actually reaches you. This sheet reports the balance a level, uninterrupted, fee-free stream of payments would reach — a benchmark to measure a real plan against, not a forecast of what one delivers.
References
- IRS Topic no. 410 — Pensions and annuities
- SEC Investor.gov — investor education and calculators
- CFPB — planning and saving for retirement
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.