A person donates $47000 today in order to provide equal annual scholarships forever, with the first scholarship awarded immediately, If the scholarship fund earns 8% compounded annually, find the amount of the annual scholarships.


I did a guess and check method using the Finance TVM solver bc I could not find a sample problem in the text.

The webassign answer is 3481.48 i just dont know how to work the problem

thanks

12/8/2006 3:23:59 PM

PV of a perpetuity = PMT/i

A perpetuity is a perpetual annuity starting one period from today so:

$47,000 = PMT/.08 + PMT (need to add one payment since scholarships start immediately)

$47,000 - PMT = PMT/.08

.08 ($47,000 - PMT) = PMT

$3,760 - .08PMT = PMT

$3,760 = 1.08 PMT

PMT = $3,760/1.08

PMT = $3,481.48

12/8/2006 3:36:10 PM

In order to last forever, the amount of $47000 can never go down.

So:
(47000 - scholarship amount) + 0.08*(47000 - scholarship amount) = 47000
so it becomes
(47000 - x) + (0.08*47000 - 0.08x) = 47000
-x + 3760 - 0.08x = 0
1.08x = 3760
x = 3,481.48

the trick is to realize immediately you're giving up the scholarship, so you have to subtract that from the principal

this coming from 10th grade algebra II

college is easy

[Edited on December 8, 2006 at 3:39 PM. Reason : second]

12/8/2006 3:37:37 PM

it's easy to say college is easy when the person before you already figured it out...

12/8/2006 4:47:02 PM

not when he is posting a min after the answer was put up. i think it would take more than a min to type that out and solve it. stop trying to make people look bad for helping others with their homework.

12/8/2006 6:46:54 PM