Suppose interest of 5% each year 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

A risk-averse individual would require a guaranteed outcome that is at least as valuable as the expected value of a risky gamble. Here, the expected value of the gamble is the average of gaining and losing $1,000, adjusted for the interest that could have been earned if the $1,000 were saved at a 5% annual interest rate for two years instead. The future value of $1,000 after two years at 5% interest compounded annually is $1,000 * (1.05)^2 = $1,102.50. To be indifferent between the gamble and the safe investment, a risk-averse person would require slightly more than this guaranteed future amount, hence $1,102.51.

Suppose Interest of 5% Each Year for Two Years Can