Annuity present value calculator

Annuity present value — the math behind structured payments

An annuity is a structured series of equal payments made at regular intervals over a defined period. The present value calculation answers a fundamental question in finance: given a stream of future cash flows, what is it worth today? This question arises every time you evaluate a pension buyout offer, a lottery lump sum vs. annual payments, a structured settlement, or the implicit return on an insurance annuity product.

Ordinary annuity vs. annuity-due

The timing of payments is critically important. An ordinary annuity (or annuity-immediate) makes each payment at the end of the period. Most loans, mortgages, and bond coupon payments follow this convention. An annuity-due makes payments at the beginning of each period — rent, lease payments, and some insurance premiums work this way.

Because annuity-due payments arrive one period earlier, each payment undergoes one less period of discounting. The result: an annuity-due is worth exactly (1 + r) times the ordinary annuity present value. On a 20-year annuity at a 5% discount rate, this difference is about 5% — meaningful when evaluating large payment streams.

Real-world applications

Pension buyouts: When a company offers to replace your defined-benefit pension with a lump sum, they're presenting you with an annuity present value calculation. Run the math: what discount rate makes the lump sum equal to the present value of the promised monthly payments? If that implied rate is higher than what you believe you can earn on the lump sum, take the pension payments.

Lottery lump sum vs. annual payments: A $50M lottery jackpot paid over 30 years at $1.67M/year is an ordinary annuity. The advertised lump sum is typically the present value of those payments, discounted at a rate the lottery authority uses (often 2.5–4%). After the 37% federal income tax haircut, the comparison changes further.

Structured settlements: Personal injury settlements are often paid as structured annuities. Plaintiffs' attorneys and defendants use present value analysis to reach agreement on the payment schedule. Secondary market companies buy structured settlements at a significant discount — the difference between market rates and contract rates is their profit.

How insurance companies price annuities

Insurance companies issuing immediate annuities price them using two inputs: a mortality table (how long you're expected to live) and an interest rate assumption (what they expect to earn on your premium). They price for the average of the population, so individuals with above-average health can extract more value; those with health issues may be better off not annuitizing. The annuity puzzle — why more people don't buy annuities despite their theoretical value — is a well-documented behavioral economics phenomenon.

QLAC: using annuities for RMD reduction

A Qualified Longevity Annuity Contract (QLAC) is a deferred income annuity purchased inside an IRA or 401(k) that is excluded from required minimum distribution (RMD) calculations until income begins (up to age 85). The SECURE Act 2.0 (2022) raised the QLAC purchase limit to the lesser of $200,000 or 25% of the account. A QLAC lets you reduce RMDs in your 70s while securing income for your 80s and beyond.

Variable vs. fixed annuity fees

Fixed annuities offer a guaranteed interest rate and are relatively simple. Variable annuities invest in mutual-fund-like subaccounts and carry significant fee loads: mortality & expense charges (0.5–1.5%), investment management fees (0.5–2%), and optional rider charges for guaranteed benefits (0.5–1.5%). Total annual fees of 2–4% on variable annuities substantially erode returns relative to a comparable taxable brokerage account with low-cost index funds. The tax deferral inside a variable annuity rarely compensates for the fee drag.