The trade-off
Pensions, structured settlements, some insurance policies and lottery jackpots often offer a choice: a lump sum now, or a series of payments over time. The payments usually add up to more, but money received later is worth less than money today. Comparing the two requires converting the payments to a present value.
The formula
For yearly payments A over n years, discounted at rate r:
Present value = A × (1 − (1 + r)^−n) ÷ r
If payments start immediately, multiply by (1 + r). If they grow by g each year, the formula becomes A × (1 − ((1 + g) ÷ (1 + r))^n) ÷ (r − g).
Worked example
A choice between $500,000 now and $40,000 a year for 20 years, starting now, with a 5% discount rate:
- Present value of the payments: about $523,413.
- The annuity is worth $23,413 more at 5%.
- Total of the payments: $800,000.
- Invested at 5%, the lump sum could pay about $38,211 a year for 20 years.
At 6%, the same payments are worth about $486,000 and the lump sum comes out ahead. The answer depends heavily on the discount rate.
Choosing the discount rate
Use the after-fee return you could realistically earn on the lump sum, at a similar level of risk. Annuity payments from a strong payer are close to risk-free, so comparing them with stock market returns overstates the value of the lump sum.
Lottery jackpots
Large U.S. jackpots advertise the annuity total, typically paid over 30 years with payments that grow by about 5% a year. The cash option is roughly the present value at current interest rates. Taxes apply either way, and taking the lump sum means paying federal tax at the top rate on the whole amount in a single year.
Other factors
- Taxes: spreading income over many years may keep you in lower brackets.
- Inflation: fixed payments lose purchasing power; cost-of-living adjustments help.
- Longevity: lifetime pensions protect against outliving your money.
- Payer risk: check the financial strength of the insurer or pension plan.
- Behavior: a lump sum offers flexibility, but only if it is invested with discipline.
This calculator gives estimates for education and planning. It is not investment, tax or legal advice; for decisions about your own situation, talk to a qualified financial professional.