Posted by tiff on Sunday, October 25, 2009 at 1:58pm.
For mark:
interest rate
= 7.5% p.a.
= 7.5%/12 per period of one month
= .625%
Future value of $5000 in n years, FVK(n)
= 5000*(1.00625)12*n
For Madonna,
interest rate
= 8.125% p.a.
= 8.125%/4 per quarter
= 2.03125% per quarter
Future value of $5000 in n years, FVD(n)
= 5000*(1.0203125)4*n
We look for n where
FVD(n) = 3FVK(n)
5000*(1.0203125)4*n
= 3*5000*(1.00625)12*n
(1.0203125)4*n / (1.00625)12*n = 3
Take log on both sides
4*n*log(1.0203125)-12*n*log(1.00625) = 3
n = log(3)/(4log(1.0203125-12log(1.00625))
= 193.785 years
Check:
in 193.785 years,
Mark will have $9,801,861,882.04
Madonna will have $29,405,482,100.99
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