Answer
$\$9513.28.$
Work Step by Step
According to the Compound Interest Formula, where $P$ is the principal, the amount deposited, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded annually, $t$ is the number of years, $A$ is the amount you get back after $t$ years: $A=P\cdot(1+\frac{r}{n})^{n\cdot t}.$
Here we have: $t=1\text{ years}$
$r=5\%=0.05$
$A=\$10000$
$n=12$ (since it is compounded monthly)
Substitute these values into the formula above to obtain:
Here $\$10000=P\cdot(1+\frac{0.05}{12})^{12\cdot 1}.$
Thus $P=\frac{10000}{(1+\frac{0.05}{12})^{12\cdot1 }}\approx\$9513.28.$
