You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 25 years and the payments will increase by 2 percent per year. If the appropriate discount rate is 6 percent, what is the present value of your winnings? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

Question

Business

Xander Lester

2 April, 08:48

You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 25 years and the payments will increase by 2 percent per year. If the appropriate discount rate is 6 percent, what is the present value of your winnings? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

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Answers (1)

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Cullen Patterson · Answer 1

PV=$15,500,000

Explanation:

To know the present value (PV) of the winnings we use the following formula:

PV = (F1 / (i-g)) * FC

F1 = Payment in t=1 (In this case it is $1,000,000 because you will receive it in one year)

i = interest rate (or discount rate: 6%)

g = growth rate (2%)

n = number of periods (25)

FC = 1-[ (1+g) / (1+i) ]^ (n)

We replace in the formula:

FC = 1-[ (1+2%) / (1+6%) ]^ (25)

FC=1-[0.382]

FC = 0.618

Rounded to 2 decimal places

FC = 0.62

PV = (1,000,000 / (6%-2%)) * 0.62

PV = (25,000,000) * 0.62

PV=$15,500,000