The 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.
This is what I have done:
$272.71= 200 (1+ (0.0625/x))^x $
$1.36355= (1+ (0.0625/x))^x $
I am unsure on how to solve for x now, because it is in two places. Any help?
There is a slip in the setting up of the equation. It should be $$272.71= 200 \left(1+ \frac{0.0625}{x}\right)^{5x}.$$ Now to the main question. There is no nice "closed form" way of solving this kind of equation. (Possibly one could use the Lambert $W$-function, but that will not be computationally useful.)
One can use a numerical method, such as the Newton Method. Much more simply, one can experiment with various values of $x$. (I got lucky and got it on the first guess.)
