A rich donor gives a hospital $100,000 one year from today. Each year after that, the hospital will receive a payment 5% larger than the previous payment, with the last payment occurring in ten years' time. What is the present value (PV) of this donation, given that the interest rate is 9%?

Question

Quizplus · Accepted Answer

To find the present value (PV) of the donation, we need to discount each future payment back to the present time (today) using the given interest rate. We can use the formula:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years in the future.

For the first payment, one year from now, FV = $100,000, r = 9%, and n = 1. Therefore:

PV1 = $100,000 / (1 + 0.09)^1
PV1 = $91,743.12

For the second payment, two years from now, FV = $100,000 x 1.05 = $105,000, r = 9%, and n = 2. Therefore:

PV2 = $105,000 / (1 + 0.09)^2
PV2 = $87,752.00

Similarly, we can calculate the present value of each future payment using the same formula:

PV3 = $91,421.68
PV4 = $85,244.44
PV5 = $79,582.63
PV6 = $74,404.88
PV7 = $69,682.19
PV8 = $65,387.06
PV9 = $61,493.69
PV10 = $57,977.08

Finally, we can add up all the present values to get the total present value of the donation:

PV = PV1 + PV2 + PV3 + PV4 + PV5 + PV6 + PV7 + PV8 + PV9 + PV10
PV = $779,843.27

Therefore, the best choice is A, $779,843.27.

A Rich Donor Gives a Hospital $100,000 One Year from Today