Question

Suppose you win $1 million in a lottery and your winnings are scheduled to be paid as follows: $400000 at the end of one year, $400000 at the end of two years, and $200000 at the end of three years. If the interest rate is 5 percent, what is the present discounted value of your winnings

Answer 1

Answer:

The present discounted value of the winnings is $916,531.69.

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.