Question

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.

Answer 1

I agree that you have a very hard equation to solve, and there is no simple algebraic method to do so

Fortunately, you know that the compounding is probably either semi-annually, quarterly, monthly, daily etc.
that is
n = 2 , 4, 12 or 365

so lets test it
let n = 2 (semi-annually)
200(1 + .03125)^10 = 272.06 , close

let n = 4
200(1 + .015625)^20 = 272.71
How about that,

So the interest rate is compounded quarterly

( confirmed by running your equation through Wolfram
http://www.wolframalpha.com/input/?i=solve+200%3D272.71%281%2B0.0625%2Fx%29%5E%28-5x%29+)