Suppose interest of 5% for two years can be earned on $1,000 saved today with no risk.What is the least amount a person would need to have a 50% chance of winning to be willing to face a 50% chance of losing $1,000 today and be considered risk averse?
A)$907.03 to be paid in two years
B)$1,000.01 to be paid in two years
C)$1,100.01 to be paid in two years
D)$1,102.51 to be paid in two years

Question

Quizplus · Accepted Answer

To solve this problem, we need to find the expected value of the amount the person would win if they took the risk.

If they win, they would receive the amount they risked plus the interest earned on that amount over two years:

$1,000 + ($1,000 * 0.05 * 2) = $1,100

If they lose, they would receive nothing:

$0

So the expected value of their winnings is:

(0.5 * $1,000) + (0.5 * $1,100) = $1,050

Therefore, the least amount the person would need to have a 50% chance of winning to be willing to face a 50% chance of losing $1,000 today is $1,050. This amount will be received in two years, so we need to discount it back to present value using the 5% interest rate:

PV = FV / (1 + r)^n

PV = $1,050 / (1 + 0.05)^2

PV = $907.03

Therefore, the best choice is (D) $1,102.51 to be paid in two years, because it is the closest option to the expected value of $1,050.

Suppose Interest of 5% for Two Years Can Be Earned