Mary is running a retirement community and is negotiating with a client, Jimmy, who wishes to reside at Mary’s community when he retires in ten years at age 65. Actuarial statistics indicate that Jimmy will probably die at age 85. Costs of caring for each client are estimated to be $15,000 per year. Jimmy’s salary is $32,000 per year. If Mary requires a $10,000 down payment today and have a 6% investment opportunity cost compounding annually, what proportion of Jimmy's annual income should he pay to Mary each year between now and when he retires? Assume that all cash flows occur at year-end (except for the down payment).
a. 30.29%
b. 36.55%
c. 32.64%
d. 31.89%
e. 34.57%
Hints: Jim has 10 years from now to make the annual deposits to pay for the 20 years cost (15,000 each year). Calculate the present value of those 15,000s, and that is how much worth in total (Jim’s annual deposits and the down payment worth) at the age of 65.