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...

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

3. You take all the information about Aunt Grace's gift to your not-quite-so-wealthy Aunt Margaret. In addition to the $1 M already deposited there byAunt Grace, how much would Aunt Margaret have to add to the fund to enable it to pay out an income stream of

R(t) = 60 +t

forever?

4. Let's revisit the income stream 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 we used in Problem 1, compute the present value of this income stream (lasting forever) assuming a constant interest rater. What is the present value of the income stream ifr= 0:02. For which values of r is the present value nite?