Annuity Calculator Formula

Understand the math behind the annuity calculator. Each variable explained with a worked example.

Formulas Used

Future Value of Annuity

fv_annuity = rate > 0 ? payment * (pow(1 + rate, n) - 1) / rate : payment * n

Present Value of Annuity

pv_annuity = rate > 0 ? payment * (1 - pow(1 + rate, -n)) / rate : payment * n

Total Payments

total_payments = payment * n

Future Value = PMT × [(1+r)^n - 1] / r

Present Value = PMT × [1 - (1+r)^-n] / r

These assume annual payments at the end of each period (ordinary annuity).

$1,000 annual payments for 20 years at 5% interest.

payment = 1000annual_rate = 5years = 20

01Future value = $1,000 × (1.05^20 - 1) / 0.05
02= $1,000 × (2.6533 - 1) / 0.05 = $33,066
03Present value = $1,000 × (1 - 1.05^-20) / 0.05
04= $1,000 × (1 - 0.3769) / 0.05 = $12,462
05Total payments = $1,000 × 20 = $20,000

Determining the fixed monthly payment on a car loan or personal loan where you borrow a lump sum and repay in equal installments.
Calculating how much you need to save each month to reach a retirement goal by a specific date, treating regular contributions as an annuity.
Comparing annuity quotes from insurance companies — converting a lump sum premium into the equivalent monthly payout helps you compare offers on equal footing.
Planning a systematic withdrawal from a retirement portfolio where you want equal monthly payments for a specific number of years.
Structuring lease payments for equipment or property where the lessor needs to recover cost plus interest over the lease term.

Confusing annuity due (payments at the beginning of each period) with ordinary annuity (payments at the end) — annuity due payments are slightly smaller for the same total because each payment has one extra period to earn interest. Using the wrong type understates or overstates payments.
Using the annual interest rate instead of the periodic rate — a 6% annual rate on a monthly annuity requires dividing by 12 to get 0.5% per month. Using 6% per month gives a wildly wrong payment amount.
Forgetting that the number of periods must match the payment frequency — a 5-year loan with monthly payments has 60 periods, not 5. This mismatch is the single most common annuity calculation error.
Ignoring the present value vs. future value distinction — the payment formula for a loan (solving for PMT from PV) is different from the formula for a savings plan (solving for PMT from FV). Using the wrong one gives an answer to a question you did not ask.

An annuity is a series of equal payments made at regular intervals. Examples include pension payments, lease payments, and insurance payouts.

Ready to run the numbers?