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You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 35 years and the payments will increase by 3.4 percent per year. If the appropriate discount rate is 7.4 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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facundobuzzetti

Answer:

Present Value= $9,003,586.40

Explanation:

Giving the following information:

You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 35 years and the payments will increase by 3.4 percent per year. The appropriate discount rate is 7.4 percent.

I will assume that 1 million is the first payment of 35.

First, we will calculate the final value. To do this, we need to sum the growing rate to the interest rate.

FV= {A*[(1+i)^n-1]}/i

A= annual deposit= 1,000,000

i= 0.074 + 0.034= 0.108

n=35

FV= {1,000,000*[(1.108^35)-1]}/0.108= $326,067,227.1

Now, we can calculate the present value:

PV= FV/ (1+i)^n

PV= 326,067,227.1/ 1.108^35= $9,003,586.40

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