Pension Lump Sum vs Annuity: Present Value, Break-Even Age & Risk Trade-offs

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Value Maya's pension annuity of $1,850 a month as a lump-sum equivalent at six discount rates and see at which rates the annuity or the $310,000 lump sum looks better.
• Turn the choice around: what return does the annuity pay on the $310,000 if Maya lives to 75, 80 … 100, and from which age does it beat a safe 4 % return?
• Track 30 years of annuity payments, cumulative and discounted, and find the age at which Maya has received more than the lump sum, without and with the time value of money.
• Value the lifetime annuity properly: each year's payment times the probability that Maya is alive to receive it, discounted, summed to the expected present value and compared with the lump sum.
• Compare a fixed $22,200 a year with a lower annuity that rises 2.5 % a year (COLA), both in nominal and in today's dollars at 3 % inflation, and chart the buying power over 30 years.
• Take the lump sum instead, withdraw the same $22,200 a year and earn 4.5 %: a year-by-year balance path, the age when the pot is empty, the years of full income and a chart of the balance.
• Test the drawdown plan against six return scenarios with probabilities: the balance left at 90 in each, which ones run dry, the probability of running out and the probability-weighted balance.
• Compare Maya's single-life pension with 50 %, 75 % and 100 % joint-and-survivor options for her husband Daniel: the reduction for each, two annuity factors from survival probabilities and the expected value for the household.