Finance

A wealthy donor endows a chaired professorship. If the interest rate is 8% how much must he set aside to provide the following end of year salary payment alternatives?
a. $100,000 per yr for 20 yrs
b. $100,000 per yr in perpetuity
c. A perpetuity that pays $100,000 for the first year and grows at 4% thereafter.

Excel to be used to solve this


You wrote, "If the interest rate is 8%" but you didn't tell us how it's compounded. So I'll assume simple interest compounded annually in the suggestions.
For a. we would need 100,000*20=2,000,000 so
2,000,000=P(1+.08)20
Solve for P
For b. you want
100,000=P*.08 since we assume the interest is fixed at 8% for perpetuity too.
For c. we want
100,000(1+.04)n=P(1+.08)n so
P=100,000* (1.04/1.08)n
This looks like a geometric series that I'll let you solve. I'll be glad to check your work. (It looks to be around 2.7mil or something close)


After rechecking the questions I'm not sure if I gave the right approach for a.
I'm not sure if I followed the question now either. Is the endowment supposed to be used entirely over that time period? I'll look at this again to see if I can make sense of it.


To solve part a. I assumed the amount was supposed to be used up completely at the end of 20yrs.
You would start with amount P, then mutiply it by 1.08 and subtract 100,000
The formula looks like (P*1.08) -100,000
I dragged that down twenty rows. Then I used the goal seek to get the twentieth row to equal 0 and pointed to another cell for the P value.
The anwer I got was P = 981,814.74

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