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 Financial Mathematics Old FM Forum

#1
01-05-2019, 01:38 PM
 morbrenn SOA Join Date: Nov 2018 Studying for FM Posts: 10
FM Question of Unknown Time

A deposits 10 today and 30 in 5 years at a simple interest rate of 11% per year. B makes the same deposits but at times n and 2n, at an annual effective rate of 9.15%. At 10 years A and B's accumulated values are equal. Calculate n.

I set up an equation of value comparing at time 10 as follows:
10(1+.11(10))+30(1+.11(5))=10(1.0915)^(10-n)+30(1.0915)^(10-2n)

and got it to here:
2.8123=(1.0915)^(-n)+3(1.0915)^(-2n)

but at this point it seems algebraically unsolvable? There's no log properties that will isolate n, so how can I solve this?
#2
01-05-2019, 01:46 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 6,057

Let x = 1.0915^-n

You'll get a quadratic in x. Find its roots. You take it from there.
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#3
01-05-2019, 01:49 PM
 Breadmaker Member SOA Join Date: May 2009 Studying for CPD - and nuttin' else! College: Swigmore U Favorite beer: Guinness Posts: 4,208

Can you express it as ax^2 + bx + c ???

Curses, ninja'd!!
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#4
01-05-2019, 01:54 PM
 morbrenn SOA Join Date: Nov 2018 Studying for FM Posts: 10

Thanks, guys. I also figured it out shortly after posting..