How to use the lump sum vs annuity calculator
- Enter the lump sum you are offered and the annuity payment with how often it is paid.
- Enter the years the payments last. For a lifetime annuity, enter the number of years you expect to collect.
- Enter a discount rate, which is what you think you could earn on the lump sum. Add a yearly increase if the payment grows.
- Read the present value of the annuity, which offer is worth more at that rate and the break even rate.
Formula
Per-period rate r = (1 + annual rate)^(1 / payments per year) - 1
Present value = sum of payment(t) / (1 + r)^t for t = 1 to n
Payments at the start of a period are divided by (1 + r)^(t - 1) instead
Break even rate = the discount rate at which present value equals the lump sum
If the payment grows, it steps up once a year by the percent you enter. The break even rate is found by repeated trial.
Worked example
You are offered $300,000 now, or $2,000 a month for 20 years (240 payments, $480,000 in total). At a 5% annual discount rate, the payments have a present value of $305,886.89, so the annuity is worth $5,886.89 more.
The break even discount rate is about 5.24%. If you think you could earn more than that on the lump sum, take the lump sum. At 7 percent the lump sum wins. For one yearly payment of $1,000 at 10%, the present value is $909.09 at period end and $1,000.00 at period start.
Why a discount rate matters
A dollar today is worth more than a dollar later because you can invest it. The discount rate expresses that. A high rate shrinks the value of later payments and favors the lump sum, and a low rate favors the annuity. There is no single right rate, so the break even rate is a useful number: it is the return you would need to earn on the lump sum to match the annuity.
What the math leaves out
A lifetime annuity pays for as long as you live, so it protects against outliving your money, which a lump sum does not. The strength of the company or plan paying the annuity matters, along with survivor benefits, inflation and taxes. A lump sum gives flexibility and may pass to heirs. Taxes on each choice can differ, and you should ask a professional.
Related tools
See payments from a lump sum in the annuity calculator, discount single amounts in the present value calculator, and check pension questions in the pension calculator. Spending in retirement is covered by the retirement withdrawal calculator.
Assumptions and limits
- Payments are fixed for the number of years you enter. A lifetime annuity is modeled as a number of years you choose.
- The discount rate is steady and is an example you should replace with your own assumption.
- Taxes, inflation, survivor benefits and the risk that the payer fails are not modeled.
- The break even rate search covers rates from -50 percent per period up to a very high rate.
Frequently asked questions
Should I take a lump sum or an annuity?
It depends on your health, your other income, how comfortable you are investing and the offer itself. Compare present values and the break even rate, and consider asking an adviser.
How do you compare a lump sum with monthly payments?
Convert the payments into today's dollars with a discount rate and compare the present value with the lump sum.
What is the break even rate?
It is the discount rate at which the annuity and the lump sum have the same present value. Earning more than that favors the lump sum.
Does it matter whether payments come at the start or end of the period?
Yes. Payments at the start of each period are worth a little more, because they arrive a period sooner.