Question

1. The California state government advertises that one of its lotteries will pay out $1 million: the

prize money is spread over twenty years in twenty equal payments.

a. If the interest rate is 10 percent and the first payment is received at the end of the current year, what is the present value of this lottery prize money?

b. Now suppose that the interest rate is 5 percent. What is the present value now?

c. Provide economic intuition for why your answers to (a) and (b) differ.

Answer 1

Answer : 1) a) The formula of present value (PV) is,

PV = FV * [ 1 / (1 + r)^n ]

Here FV = Future Value = $1 million = $1,000,000

r = interest rate = 10% = 0.1

n = number of years = 20 years

Now,

PV = 1000000 * [ 1 / (1 + 0.1)^20 ]

=> PV = 1000000 * (1 / 6.727)

=> PV = 148654.675

Therefore, the present value of lottery prize is $148654.675 .

b) Now, if r = 5% = 0.05,

PV = 1000000 * [ 1 / (1 + 0.05)^20 ]

=> PV = 1000000 * [ 1 / 2.653 ]

=> PV = 376931.775

Therefore, the present value of lottery prize is $376931.775 .

c) Here the answers of (a) and (b) are different due to differences in interest rate. As the interest rate is low in (b) than (a), hence the present value of lottery is higher in (b) than (a).