Question

A lottery claims its grand prize is ​$5 ​million, payable over 5 years at ​$1 comma 000 comma 000 per year. If the first payment is made​ immediately, what is the grand prize really​ worth? Use an interest rate of 4​%.The real value of the grand prize is ​$nothing. ​(Round your response to the nearest​ dollar.)

Answer 1

present value of the prize: 4,451,822 dollars

Step-by-step explanation:

we will calcualte the present value of an annuity-due of 5 payment of 1,000,000 discount at 4%

`C * (1-(1+r)^(-time) )/(rate)(1+r) = PV\\`

C 1,000,000

time 5

rate 0.04

`1000000 * (1-(1+0.04)^(-5) )/(0.04)(1+0.04) = PV\\`

PV $4,451,822.3310

This will be the present value of the prize today