Question

4.

Answer 1

To solve this we are going to use the present value of annuity formula: $PV=P[ \frac{1-(1+ \frac{r}{n})^{-kt} }{ \frac{r}{n} } ]$
where
$PV$ is the present value 
$P$ is the periodic payment 
$r$ is the interest rate in decimal form 
$n$ is the number of times the interest is compounded per year 
$k$ is the number of payments per year 
$t$ is the number of years 

We know from our problem that $P=4725$ and $t=15$. To convert the interest rate to decimal form, we are going to divide it by 100%:
$r= \frac{10}{100}$
$r=0.1$
Since the interest is compounded semiannually, it is compounded 2 times per year; therefore, $n=2$. Similarly, since the payment is made at the end of each 6 months, it is made 2 times per year; therefore, $k=2$.
Lest replace the values in our formula:

$PV=P[ \frac{1-(1+ \frac{r}{n})^{-kt} }{ \frac{r}{n} } ]$
$PV=4725[ \frac{1-(1+ \frac{0.1}{2})^{-(2)(15)} }{ \frac{0.1}{2} } ]$
$PV=72634.83$

We can conclude that the correct answer is $72,634.83