Question

2.

Answer 1

To solve this we are going to use the future value of annuity due formula: $FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]$
where
$FV$ is the future 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 for our problem that $P=295$ and $t=6$. To convert the interest rate to decimal for, we are going to divide the rate by 100%:
$r= \frac{10}{100}$
$r=0.1$
Since the payment is made quarterly, it is made 4 times per year; therefore, $k=4$.
Since the type of the annuity is due, payments are made at the beginning of each period, and we know that we have 4 periods, so $n=4$.
Lets replace those values in our formula:

$FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]$
$FV=(1+ \frac{0.1}{4} )*295[ \frac{(1+ \frac{0.1}{4} )^{(4)(6)} -1}{ \frac{0.1}{4} } ]$
$FV=9781.54$

We can conclude that the amount of the annuity after 10 years is $9,781.54