A lottery claims its grand prize is $15 million, payable over 5 years at $3000000 per year. If the first payment is made imm

Question

3 years ago

15

ediately, what is the grand prize really worth? Use an interest rate of 8%.

1 answer:

xz_007 [3.2K] · Answer 1 · 2021-12-08T08:41:27+03:00

Answer:

$ 11, 978,133.75

Explanation:

The grand prize of 15,000,000 is worth the present value of the prize at an 8% interest. The prize is paid every year, meaning its an annuity case.

The present value of an annuity is calculated using the formula

PV = P × 1 − (1+r)−n

r

Where

P $3,000,000

r is 8% 0r 0.08

n is 5

PV = $3,000,000 x 1-(1+0.08) - 5

0.08

PV =$3,000,000 x 1 - 0. 6805831

0.08

PV = $ 3,000, 000 x 3.99271

PV = 11, 978,133.75

A lottery claims its grand prize is ​$15 ​million, payable over 5 years at ​$3000000 per year. If the first payment is made​ imm