Annuity Calculator
This annuity calculator values a stream of equal periodic payments, returning both the present value (what the whole stream is worth today) and the future value (what it accumulates to by the end). You supply the payment amount, the rate per period, the number of periods, and whether payments arrive at the end of each period (ordinary annuity) or the start (annuity due). Switching to annuity due multiplies both results by one plus the rate, because every payment earns or is discounted for one extra period.
Formula
PV = PMT·(1 − (1 + r)^−n)/r ; FV = PMT·((1 + r)^n − 1)/r
- PMT
- Payment made each period
- r
- Interest rate per period (decimal = rate% ÷ 100)
- n
- Total number of payment periods
- PV / FV
- Present and future value; multiply each by (1 + r) for an annuity due
How it works
- Enter the regular payment, the interest rate per period, and the total number of periods. The rate and periods are treated on the same per-period basis, so an annual payment uses an annual rate.
- Choose the annuity type. An ordinary annuity assumes payments at the end of each period; an annuity due assumes payments at the beginning, which is handled by scaling the values by (1 + rate).
- The calculator returns the present value using the discounting formula and the future value using the accumulation formula, letting you compare a lump sum today against the same payments invested over time.
Worked example
An ordinary annuity paying $5,000 per year for 20 years at 5% per period.
- Per-period rate r = 5 ÷ 100 = 0.05; periods n = 20.
- PV = 5,000 × (1 − 1.05^−20) ÷ 0.05 = 5,000 × 12.4622 = $62,311.05.
- FV = 5,000 × (1.05^20 − 1) ÷ 0.05 = 5,000 × 33.0660 = $165,329.77.
The stream is worth about $62,311.05 today and grows to roughly $165,329.77 after 20 years. As an annuity due, both rise by 5% to about $65,426.60 and $173,596.26.
Frequently asked questions
- What is the difference between an ordinary annuity and an annuity due?
- In an ordinary annuity each payment is made at the end of the period; in an annuity due it is made at the beginning. Paying earlier means every payment compounds or is discounted for one more period, so this tool multiplies both present and future value by (1 + r) for an annuity due.
- Should the rate be annual or monthly?
- It must match the payment frequency. The calculator uses one rate per period and one count of periods, so for monthly payments enter the monthly rate and the number of months, and for annual payments enter the annual rate and the number of years.
- Why is the present value lower than the total of all payments?
- Money received in the future is worth less than money today, so each payment is discounted back at the period rate. Twenty $5,000 payments total $100,000 nominally, but their present value is lower because the later payments are discounted more heavily.