Answer
a. $A(384)= 5,027,378,918.03$
b. $A384t)=5,231,970,592.30$
Work Step by Step
a. The formula for monthly compounded interest is,
$A(t)=P(1+\frac{r}{n})^{nt}$. Whereas, $n$ is the number of times the interest is compounded in a year which in this case is $12$, $P$ is the initial investment, $t$ is time and $r$ is rate.
In this case, we are given that.
$n=12$,
$t=2010-1626=384$,
$r=0.05$,
$P=24$
$A(384)=24(1+\frac{0.05}{12})^{12\times 384}= 5,027,378,918.03$
b.The formula for continuously compounded interest is,
$A(t)=Pe^{rt}$, whereas $e$ is the natural logarithm constant, $r$ is rate, $t$ is time and $P$ is the initial investment.
In this case, we are given that,
$r=0.05$
$t=2010-1626=384$
$P$ is the initial investment.
therefore,
$A(384)=24\times e^{0.05\times 384}=5,231,970,592.30$
