How the Immediate Annuity Calculator works
A single-premium immediate annuity (SPIA) converts a lump sum you pay an insurer today into a stream of income payments that begins right away — typically with the first payment landing within the first period, rather than years later like a deferred annuity. This calculator answers the core question behind an SPIA quote: given a premium, a discount rate, and a payout term, how large is each income payment?
The formula
For a premium P, a periodic discount rate i (the annual rate divided by payments per year), and n total payments (years × payments per year), the payment is:
PMT = P × i / [(1 − (1 + i)−n) × (1 + i)]
This is the annuity-due version of the standard present-value annuity payment formula. It differs from an ordinary annuity (used for loans or payouts that start after a delay) by the extra (1 + i) factor in the denominator, which shifts each payment to the start of its period instead of the end — because "immediate" means income begins as soon as the contract is purchased. If the discount rate is 0%, the formula reduces to PMT = P / n, the premium split into equal installments with no interest earned. The calculator assumes the balance compounds at the payment frequency and reaches exactly zero at the end of the chosen term.
Worked example
Take a $200,000 premium at a 4% annual discount rate, paid monthly for 15 years. The periodic rate is 0.04 / 12 ≈ 0.003333 and n = 180 payments. The formula gives a payment of about $1,474 per month. Over the full 15 years that totals roughly $265,400 — the original $200,000 premium plus about $65,400 of interest earned on the balance that had not yet been paid out. (For comparison, the same inputs run through the ordinary, end-of-period formula would pay about $1,479 per month — annuity-due payments are slightly smaller because each one arrives a period earlier.)
What moves the payment most
- Payout length: spreading the same premium over more years lowers each payment but raises the total received, because the remaining balance keeps earning interest for longer.
- Discount rate: a higher rate lets the same premium support a larger payment. At 0% the $200,000 example pays only $1,111 per month; at 4% it pays about $1,474.
- Frequency: monthly, quarterly, and annual schedules of the same annual amount differ only slightly — more frequent payments draw the balance down a little sooner, so each year's total is marginally smaller.
Immediate versus deferred, and fixed-term versus lifetime
"Immediate" refers to when payments start, not how long they last. This calculator models a fixed-period (term-certain) immediate annuity: payments start now and stop after the chosen number of years regardless of how long you live. Insurers also sell lifetime immediate annuities, which guarantee income for life and are priced using mortality tables, fees, and guarantee riders in addition to the discount rate — so an insurer's quote for the same premium will not match this pure interest-and-principal math. Use the result here as a transparent baseline to compare against annuity quotes.