Answer:
The present discounted value of the winnings is $916,531.69.
Step-by-step explanation:
The present discounted values of each of the payment can be calculated using the present value formula as follows:
PV = FV / (1 + r)^n ...................... (1)
Where;
PV = Present discounted value of payment at the end of specified year(s)
FV = Future value or the scheduled amount
r = interest rate
n = year in which the payment is scheduled to be paid
Using equation (1), we have:
PV of payment at the end of one year = $400000 / (1 + 5%)^1 = $380,952.38
PV of payment at the end of two years = $400000 / (1 + 5%)^2 = $362,811.79
PV of payment at the end of three years = $200000 / (1 + 5%)^3 = $172,767.52
The present discounted value of the winnings can now be calculated as the additions of the 3 PVs above as follows:
PV of the winnings = PV of payment at the end of one year + PV of payment at the end of two years + PV of payment at the end of three years = $380,952.38 + $362,811.79 + $172,767.52 = $916,531.69
Therefore, the present discounted value of the winnings is $916,531.69.