Question

A prize fund is set up with a single investment of $5000 to provide an
annual prize of $500. The fund is invested to earn interest at a rate of 7%
compounded annually. If the first prize is awarded one year after the initial
investment, find the number of years for which the prize can be awarded
before the fund falls below $500.

Answer 1

PV of n year annuity
5000=500*(1-1/1.07^n)/0.07
5000=7143*(1-1/1.07^n)
0.70=(1-1/1.07^n)
1/1.07^n=0.3
3.33=1.07^n
taking 'ln' both side
Ln(3.33)=Ln(1.07^n)=(n)Ln(1.07)
n=Ln(3.33)/Ln(1.07)
n=1.20/0.068
n=17.7

17 years; not enough money in year 18

Answer 2

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