1. 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?
2. Suppose Aunt Grace wanted to give annual increases of $2000 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.
3. You take all the information about Aunt Grace's gift to your not-so-quite wealthy Aunt Margaret. In addition to the $1 M, already deposited there by Aunt Grace, how much would Aunt Margaret have to add to the fund to enable it to pay an income stream of R(t)=60+t forever?
4. Let's revisit the income steam from your endowment to SCU in the first problem, which is $50 K per year with 3% continuously compounded annual increase. Instead of the 5% investment rate wae used in problem 1, compute the present value of this income stream (lasting forever) assuming a constant interest rate r. What is the prseent value of the income stream if r=0.02. For which values of r is the present value finite?
5. The present value of a perpetuity that will pay out $10K per year forever is $250K. Assuming that the interest rate is constant, find the rate.