2.Find the amount of the annuity.Amount of Each Deposit: $295Deposited: QuarterlyRate per Year: 10%Number of Years: 6Type of Annuity: Due$9,671.28$9,542.97$10,076.54$9,781.54

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

We know for our problem that [tex]P=295[/tex] and [tex]t=6[/tex]. To convert the interest rate to decimal for, we are going to divide the rate by 100%:
[tex]r= \frac{10}{100} [/tex]
[tex]r=0.1[/tex]
Since the payment is made quarterly, it is made 4 times per year; therefore, [tex]k=4[/tex].
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 [tex]n=4[/tex].
Lets replace those values in our formula:

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

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