What is the current value of her winnings?

Question

Rita Gonzales won the $62 million lottery. She is to receive $2.8 million a year for the next 20 years plus an additional lump sum payment of $6 million after 20 years. The discount rate is 14 percent.

Answer 1

Let’s look at the $6M payable in 20 years’ time.

The present-day value we will call L (for lump sum). If L had been invested at 14% now it would have grown to $6M in 20 years (annually compounded), so L(1.14)²⁰=6000000, making L=6000000/1.14²⁰=$436570 approx.

Now consider the annual payouts.

The first annual payout has a present-day value of 2800000/1.14, the second payout is 2800000/1.14², and so on up to 20 years. The total is 2800000(1/1.14+1/1.14²+1/1.14³+...+1/1.14²⁰), which is a geometrical progression, the sum of which is (2800000/1.14)(1-(1/1.14²⁰))/(1-(1/1.14))=$18544766 approx.

The total value today is therefore $436570+$18544766=$18,981,336 approx.