Calculate the future and present value of an annuity — a stream of equal payments — given the payment, interest rate, term, and frequency. Supports ordinary annuities and annuities-due.
Future & present value
An annuity is a series of equal payments made at regular intervals. Its future value is what the payment stream grows to by the end of the term (useful for savings goals), while its present value is what that future stream is worth in today's dollars (useful for valuing a pension or settlement). An ordinary annuity pays at the end of each period; an annuity-due pays at the start, so each payment compounds one extra period and produces slightly larger values.
For example, saving $500 a month for 20 years at a 6% annual rate (compounded monthly) grows to a future value of about $231,000, of which $120,000 is your contributions and the rest is interest. The present value of that same stream is about $69,800. Annuities underpin retirement income, structured settlements, lottery payouts, and loan amortization.
What your stream of payments grows into by the end — the savings-goal view of an annuity.
What the future payment stream is worth today — used to value pensions, settlements, and payouts.
Ordinary pays at period end; due pays at the start. Annuity-due values are higher by one period's growth.
An annuity in the accumulation sense is simply a stream of equal payments, and the future value formula tells you what that stream becomes. The distinction between an ordinary annuity and an annuity due is worth understanding: payments at the end of each period versus the beginning. An annuity due is worth exactly (1 + r) times more, because every payment gets one extra period of growth. Rent and insurance premiums are annuities due; most savings contributions and loan payments are ordinary annuities, which is the default assumption in nearly every calculator.
Ordinary annuity FV = PMT × [ ((1 + r)^n − 1) ÷ r ]Annuity due FV = Ordinary FV × (1 + r)Present value = PMT × [ 1 − (1 + r)^−n ] ÷ rwhere:
Assumptions: This covers the mathematical annuity. Insurance-company annuity products add mortality pooling, surrender charges and rider fees, and their quoted returns are not directly comparable to this calculation.
Compute an ordinary annuity, then show what paying at the start of each month is worth.
Result$231,020 ordinary — $232,176 if paid at the start of each month
The $1,155 gap is exactly one period of growth on the whole balance, and it scales with the rate. At 10% the same switch would be worth $3,164. It is a small effect monthly and a meaningful one for annual contributions, where contributing in January rather than December earns a full year of extra growth.