Answer
$5.5\%$ compounded semiannually yields the greater return.
Work Step by Step
After t years, the balance, A, in an account with principal P and annual interest rate r (in decimal form), compounded n times per year is:
$\displaystyle \quad A=P(1+\frac{r}{n})^{nt}$
---
Apply the formula for
$5.5\%$ compounded semiannually (n=2):
$ A=5000(1+\displaystyle \frac{0.055}{2})^{2(5)}=6558.26$
$5.25\%$ compounded monthly (n=12):
$ A=5000(1+\displaystyle \frac{0.0525}{12})^{12(5)}=6497.16$
$5.5\%$ compounded semiannually yields the greater return.
