3.Every 6 months, Reuben Lopez puts $420 into an account paying 10% compounded semiannually.Find the account balance after 15 years.$29,299.53$27,904.32$31,500.00$29,315.00

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 deposit 
[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 deposits per year

We know for our problem that [tex]P=420[/tex] and [tex]t=15[/tex]. To convert the interest rate to decimal form, we are going to divide the rate by 100%: [tex]r= \frac{10}{100} =0.1[/tex]. Since Ruben makes the deposits every 6 months, [tex]k=2[/tex]. The interest is compounded semiannually, so 2 times per year; therefore, [tex]k=2[/tex].
Lets replace the 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}{2} )*420[ \frac{(1+ \frac{0.1}{2})^{(2)(15)}-1 }{ \frac{01}{2} } ][/tex]
[tex]FV=29299.53[/tex]

We can conclude that the correct answer is $29,299.53