Annuity or lump sum, which payout is worth more.

Method and sources

Formulas: payments are monthly, in arrears. Present value = sum of each payment divided by (1 + monthly rate) to the month number, where the monthly rate is (1 + annual rate) to the power 1/12, minus 1. The step-up raises the payment once each year. Break-even month is the first month the running total of payments (or of discounted payments) reaches the lump sum. The implied return is the annual rate at which the present value of the payments equals the lump sum, found by bisection.

Reading it: if the implied return is higher than what you expect to earn safely, the annuity is the better deal on these terms; if it is lower, the lump sum is. A payout that ends at death, or one that continues to a survivor, changes the answer: set the period to the years you realistically expect to collect.

This is a pure calculation from the numbers you enter; it uses no outside data. Taxes, longevity risk, survivor benefits and inflation protection are not modelled. Not financial advice.

FAQ

How do I know if an annuity beats a lump sum?

Compare the implied return with what you could earn on the lump sum. If the payments are equivalent to a return above your own expected return, the annuity wins on pure numbers.

What does break-even mean?

It is the month by which the payments received add up to the lump sum. Beyond that month the annuity has paid out more than the lump sum, ignoring the time value of money.

What discount rate should I enter?

Use the return you could realistically earn on the lump sum without taking more risk than the annuity carries. A guaranteed bond or GIC rate is a common choice.

Why does the payout period matter so much?

A longer period means more total payments and a higher implied return. If the annuity stops at death, the period you actually collect is uncertain, so test a few lengths.