Question

1. a) You decide to give SCU an endowment that will pay out $50 K per year forever, with a continuously compounded annual increase of 3%. Assuming that you can lock in an interest rate of 5%, figure out how much this endowment would cost. What is the total value of this income stream?

b) Suppose Aunt Grace wanted to give annual increases of $2,000 per year. How would this change the computations above? Give values for the amount Aunt Grace would have to pay to fund the income stream for 25 years, 50 years, 100 years, 200 years, and forever. (Hint: You need only integrate by parts once.)

Answer 1

Ques. You decide to give SCU an endowment that will pay out $50 K per year forever, with a continuously compounded annual increase of 3%. Assuming that you can lock in an interest rate of 5%, figure out how much this endowment would cost. What is the total value of this income stream?

Ans. Amount to be contributed to endowment = 50000/(0.05-0.03)

= $ 2,500,000

Cost of endowment fund would be $ 2,500,000 initially.

It is not possible to determine the total value because it is perpetuity i.e., it will pay forever. So, there is no fixed time period. However, present total value of this income stream is $ 2,500,000.

Note: As per answering rules only one question is answered. If you want solution of other question, please upload it separately.