A lottery claims its grand prize is $15 million, payable over 5 years at $3000000 per year. If the first payment is made immediately, what is the grand prize really worth? Use an interest rate of 8%.

$ 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

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