Answer
$\$2,955.39$
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 the loaner gets back after $t$ years: $A=P\cdot(1+\frac{r}{n})^{n\cdot t}.$
Here we have:
$t=0.5\text{ years}$
$r=3\%=0.03$
$A=\$3000$
$n=12$ (since it is compounded monthly)
Substitute these values into the formula above to obtain:
$\$3000=P\cdot(1+\frac{0.03}{12})^{12\cdot 0.5}\\
\$3000=P\cdot(1+0.0025)^{6}\\
\dfrac{3000}{(1+0.0025)^{6}}=P\\
\$2955.39114=P\\
P\approx \$2955.39$
