Question

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.)

Answer 1

PV=$15,500,000

Step-by-step 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