Annuity Calculator
A level stream of payments has two values — what it grows into, and what it is worth today. Both are here, for ordinary annuities and annuities due, with the timing stated.
A stream of payments has two prices
Twenty years of $500 a month is not 'worth $120,000' in any single sense: it grows into one figure if invested (future value) and is worth a smaller figure if sold or priced today (present value). Both prices depend on one detail novices miss — whether each payment lands at the start or the end of its period.
FV = C × ((1 + r)n − 1) ÷ r · PV = C × (1 − (1 + r)−n) ÷ r · annuity due: multiply by (1 + r)
Example: $500 a month for 20 years at 6%: payments total $120,000; they grow into about $231,000 (ordinary annuity) and are worth about $69,800 today. As an annuity due — payments at each month's start — both figures rise by exactly one month's interest factor.
Ordinary vs due is not pedantry
Rent is an annuity due (paid at the start); loan payments are ordinary (at the end). Insurance annuities, leases and pensions each have their convention, and swapping them misprices the stream by a full period's interest — small per payment, material across decades of them.
How this is calculated
Level payments, nominal rate divided by the periods per year, using the closed-form annuity factors above. 'Due' timing multiplies the ordinary result by (1 + period rate) — exactly one extra period of growth on every payment. Payments total and the interest component are shown so the stream's anatomy stays visible.
Frequently asked questions
Is this the same annuity as an insurance annuity?
The mathematics is the insurance product's skeleton: an immediate annuity is a present value calculation turned into a purchase. The product adds mortality pooling, fees and guarantees that this pure calculation does not model.
Why is present value so much smaller than the payments total?
Because each future payment is discounted for its whole wait. At 6%, a payment 20 years out is worth about 30 cents on the dollar today — that shrinkage, summed, is the PV.
What if payments grow over time?
That is a growing annuity — a different formula (used for pensions with COLA and dividend projections). The pension and dividend calculators carry their own growth Versions of this arithmetic.
Can this value a lottery or settlement?
The PV mode is exactly the right shape: enter the payment, the schedule and your discount rate. The choice of rate is the entire negotiation — see the present-value page on picking it.
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