Answer
$8.25\%$ Compounded quarterly.
Work Step by Step
Investment $P=\$6,000$.
Time $t=4$ years.
$8.25\%$ Compounded quarterly $(n=4)$
Rate of interest $r=8.25\%=0.0825$.
Compounded interest formula
$A=P\left ( 1+\frac{r}{n} \right )^{nt}$
Substitute all values.
$A_1=6,000\left ( 1+\frac{0.0825}{4} \right )^{4\cdot 4}$
$A_1=6,000\left ( \frac{4+0.0825}{4} \right )^{16}$
$A_1=6,000\left ( \frac{4.0825}{4} \right )^{16}$
$A_1=6,000\left ( 1.38630641625 \right )$
$A_1=8317.83849752$.
$8.3\%$ Compounded semiannually $(n=2)$
Rate of interest $r=8.3\%=0.083$.
Compounded interest formula
$A=P\left ( 1+\frac{r}{n} \right )^{nt}$
Substitute all values.
$A_2=6,000\left ( 1+\frac{0.083}{2} \right )^{2\cdot 4}$
$A_2=6,000\left ( \frac{2+0.083}{2} \right )^{8}$
$A_2=6,000\left ( \frac{2.083}{2} \right )^{8}$
$A_2=6,000\left ( 1.38444017722 \right )$
$A_2=8306.6410633$.
By comparing both values
$A_1>A_2$.
