Answer
(a)$\$13,116.51$ .
(b)$\$13,157.04$ .
(c)$\$13,165.31$ .
Work Step by Step
Compounded interest formula is
$A=P\left ( 1+\frac{r}{n} \right )^{nt}$.
Where $A$ is the accumulated value.
Given values are
Investment $P=\$10,000$.
Time $t=5$ years.
Rate of interest $r=5.5\%=0.055$.
(a.) Compounded semiannually $(n=2)$.
Substitute all values into the formula.
$A=10,000\left ( 1+\frac{0.055}{2} \right )^{2\cdot 5}$
$A=10,000\left ( \frac{2+0.055}{2} \right )^{10}$
$A=10,000\left ( \frac{2.055}{2} \right )^{10}$
$A=10,000\left ( 1.0275 \right )^{10}$
$A=10,000\left ( 1.31165103259 \right )$
$A=13116.5103259$
Rounded to the nearest cent.
$A=\$13,116.51$ .
(b.) Compounded monthly $(n=12)$
$A=10,000\left ( 1+\frac{0.055}{12} \right )^{12\cdot 5}$
$A=10,000\left ( \frac{12+0.055}{12} \right )^{60}$
$A=10,000\left ( \frac{12.055}{12} \right )^{60}$
$A=10,000\left ( 1.00458333333 \right )^{60}$
$A=10,000\left ( 1.31570377254 \right )$
$A=13157.0377254$
Rounded to the nearest cent.
$A=\$13,157.04$ .
(c.) Compounded continuously
The formula is $A=Pe^{rt}$.
Substitute all values.
$A=10,000 e^{0.055\cdot 5}$
$A=13165.3067487$
Rounded to the nearest cent.
$A=\$13,165.31$ .
