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ToxicBug

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A sum of 10,000 was invested on September 1, 1970 at an effective annual interest rate of 5% in order to provide an annual scholarship of 2000 every September 1 forever, starting as soon as possible. In what year will the first payment of 2000 be made? What smaller payment could be made one year earlier while still permitting the annual scholarships of 2000 thereafter? Assume that interest is credited every August 31.

First of all I found how much time it would take for the investment to reach the present value of the perpetuity:

10000(1 + i)^n = 2000/i

10000(1 + 0.05)^n = 2000/0.05

n = ln(4)/ln(1.05)

n = 28.41339817

Then for the second part I did this:

X + 10000(1.05)^(28.41339817 - 1) = 2000/0.05

X = 1904.7618

But the answer in the back of the book is 1161.36

Anyone know what is my mistake?