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Financial Mathematics Old FM Forum

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Old 01-05-2019, 01:38 PM
morbrenn morbrenn is offline
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Default 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?
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Old 01-05-2019, 01:46 PM
Colymbosathon ecplecticos's Avatar
Colymbosathon ecplecticos Colymbosathon ecplecticos is offline
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Let x = 1.0915^-n


You'll get a quadratic in x. Find its roots. You take it from there.
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Old 01-05-2019, 01:49 PM
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Can you express it as ax^2 + bx + c ???

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Old 01-05-2019, 01:54 PM
morbrenn morbrenn is offline
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Thanks, guys. I also figured it out shortly after posting..
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