Answer
(a). $n=2$.
$A(t)=16081.15$
(b). $n=12$.
$A(t)=16178.18$
(c). $n=365$.
$A(t)=16197.64$
(d)., $A(t)=Pe^{rt}$
$A(t)=16198.31$
Work Step by Step
The formula for periodically compounded interest rate is, $A(t)=P(1+\frac{r}{n})^{nt}$. Whereas, $P$ is the Initial investment, $r$ is the rate, $n$ is a number of times it is compounded.
Meanwhile, The formula for continuously compounded interest rate is, $A(t)=Pe^{rt}$.
Thus, $P=12000$, $r=0.1$, $t=3$.
(a). $n=2$.
$A(t)=12000(1+\frac{0.1}{2})^{2\times3}=16081.15$
(b). $n=12$.
$A(t)=12000(1+\frac{0.1}{12})^{12\times3}=16178.18$
(c). $n=365$.
$A(t)=12000(1+\frac{0.1}{365})^{365\times3}=16197.64$
(d)., $A(t)=Pe^{rt}$
$A(t)=12000e^{0.1\times3}=16198.31$
