Answer
a. $A(t)=12000(1+0.056/12)^{12t}$,
b. $A(3)=14195.06$
c. $t=9.122$
Work Step by Step
-The formula for periodically compounded interest is,
$A(t)=P(1+r/n)^{nt}$. Whereas, $P$ is the Initial Investment, $r$ is the rate of growth, and $n$ is number of times it compounds.
-The formula for continuously compounded interest is,
$A(t)=Pe^{rt}$
$P=12000$, $r=0.056$
a. $A(t)=12000(1+0.056/12)^{12t}$,
b. $A(t)=12000(1+0.056/365)^{365t}$,
$A(3)=12000(1.0001534)^{1095}$,
$A(3)=14195.06$
c. $A(t)=12000e^{0.056t}=20000$,
$e^{0.056t}=1.666$
$0.056t=\ln(1.666)$,
$t=\frac{\ln(1.666)}{0.056}$,
$t=9.122$
