EXAMPLE 13 Winning a Lottery

The world record lottery jackpot with a single winner was $370.9 million in May 2013. The winner had the option of receiving the “annuity value” of the prize, $590.5 million, in 30 graduated annual installments, the first payment being right away. To take into account inflation, each installment was to be 4% larger than the previous one. However, the winner chose instead the instant lump sum of $370.9 million. Well, she was 84 years old at the time … (but had she chosen the annuity, after her death any remaining payments would have been made to her estate). What was the interest rate of the annuity?

We don’t offer a solution here. In the past, lotteries used to offer annuities with level payments over 25 to 30 years. For such an annuity, we could use the amortization formula and software to determine the effective interest rate on which the payments are based. Now the annuities offered by lotteries usually feature graduated payments (4% or 5% per year), a situation that offers more complications than we want to go into here. Such calculations are commonly handled by actuaries (see Spotlight 22.4).