Financial Math Problem

[d1zzy07]

The accumulated value of a capital of K dollars that was invested for n years is 30 474.91$ at the nominal discount rate of 4% per year capitalized every trimester while the actual value of 2K dollars payable in 3n years is 13 089.11$ at the nominal interest rate of 6% per year capitalized every month. Find the actual value of K dollars payable in n years at the instant interest rate of 3% per year.

So far I got:

K(1-1%)^-4n = 30 474.91 (because 4% per year capitalized every trimester is 1% every trimester and there's 4n trimesters in n years.)

2K(1+0.5%)^-36n = 13 089.11 (because 6% per year capitalized every month is 0.5% per month and there's 36n months in 3n years.)

But now I'm having trouble isolating n or K.

 

[tkhunny]

Trimester - Tricky word. In is NOT 1/3 of a year. It is 3 months, making it the same as Quarterly.

You have it. What's the hangup?

\(\displaystyle K = 30474.91\cdot\left(1-\frac{0.04}{4}\right)^{4n}\)

There, it's isolated. Also,

\(\displaystyle K = 6544.555\cdot\left(1+\frac{0.06}{12}\right)^{36n}\)

Equating the two more complicated values, then, one easily solves for n using perhaps logarithms.