Juan has just received a prize which entitles him to receive annual payments of $10,000 at the end of each year for the next 10 years. He would like to sell the rights to the prize money to a financial institution, so that he can have the cash now. In order to estimate the present value of the prize, he will use a discount rate of 5%. What is the present value of the prize?

Question

Quizplus · Accepted Answer

The present value of the prize is equal to the discounted value of each annual payment added together. To calculate the discounted value of each payment, we can use the formula:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value (in this case, $10,000), r is the discount rate (5%), and n is the number of years in the future (1 for the first year, 2 for the second year, etc.).

Using this formula, we can calculate the discounted value of each payment:

PV year 1 = $10,000 / (1 + 0.05)^1 = $9,523.81
PV year 2 = $10,000 / (1 + 0.05)^2 = $9,070.29
PV year 3 = $10,000 / (1 + 0.05)^3 = $8,623.21
PV year 4 = $10,000 / (1 + 0.05)^4 = $8,182.51
PV year 5 = $10,000 / (1 + 0.05)^5 = $7,748.13
PV year 6 = $10,000 / (1 + 0.05)^6 = $7,320.02
PV year 7 = $10,000 / (1 + 0.05)^7 = $6,898.10
PV year 8 = $10,000 / (1 + 0.05)^8 = $6,482.27
PV year 9 = $10,000 / (1 + 0.05)^9 = $6,072.47
PV year 10 = $10,000 / (1 + 0.05)^10 = $5,668.61

Adding these values together, we get the present value of the prize:

PV = $9,523.81 + $9,070.29 + $8,623.21 + $8,182.51 + $7,748.13 + $7,320.02 + $6,898.10 + $6,482.27 + $6,072.47 + $5,668.61
PV = $71,080.32

Therefore, the best choice is C.

Juan Has Just Received a Prize Which Entitles Him to Receive