Deferred Annuity Calculator

How it works

PV = PMT × aₙ × (1 + i)⁻ᵈ · aₙ = [1 − (1 + i)⁻ⁿ] ÷ i (× (1 + i) if payments are at the beginning of each period) · i = annual rate ÷ payments per year, d = deferral periods, n = number of payments · PMT = lump sum ÷ [aₙ × (1 + i)⁻ᵈ]

A deferred annuity is a series of equal payments that begins only after a waiting (deferral) period — for example, a pension that starts in five years or a college fund that pays out tuition later. Its value today is the value of an ordinary annuity at the start of the payout period, discounted back over the deferral period. With end-of-period payments and a deferral of d periods, the first payment arrives at the end of period d + 1; with beginning-of-period payments it arrives at the start of period d + 1. The same formula, solved for the payment, shows how much income a lump sum invested today can provide later.

Worked example

Monthly payments of 1,000 for 10 years (120 payments) that start after a 5-year deferral, at 6% a year (0.5% a month): when the payout begins the annuity is worth 1,000 × [1 − 1.005⁻¹²⁰] ÷ 0.005 = 90,073.45. Discounting that over the 60 deferral months with 1.005⁻⁶⁰ = 0.741372 gives a present value of 66,777.95. You would receive 120,000 in total, of which 53,222.05 is interest.

Sources: Wikipedia — Annuity (finance theory) · Investor.gov — Annuities

Frequently asked questions