Financial Math Help? (Determine compound period)?
Future value of a $200 deposit in an account that earns 6.25% annual interest is $272.71 after 5 years. Determine the compounding period for this investment.
My work:
PV=FV(1+I/n)^ (-n)
200=272.71(1+0.0625/n)^-5n
log0.73=log(1+0.0625/n)-5n
This is where I got stuck. No idea how to continue
The answer is that it is compounded quarterly.
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Verified answer
FV = PV(1+i/n)^5n
5n ln(1+i/n) = ln(FV/PV)
n ln(1+i/n) = 0.2 ln(FV/PV)
Note that ln(1+x) can be approximated as a power series x - x^2 / 2 for small x (I am using only the first 2 terms of the power series approximation here). I am using natural logarithms (ln) rather than log (base 10) form. Inserting this approximation into the above, we have:
n (i/n - 0.5 i^2/n^2) = 0.2 ln(FV/PV)
i - 0.5 i^2/n = 0.2 ln(FV/PV)
i^2/n = 2(i - 0.2 ln(FV/PV)
n=i^2 / 2(i - 0.2 ln(FV/PV) = 4.05 (approximately 4)