Question

I'm sorry but these are the multiple choice answers.

Find the future value of the annuity due for $200 deposited at the beginning of each quarter for 12 years at 7% compounded quarterly.

A) 3,828.13
B) 14,652.56
C) 14,200.55
D) 15,112.48

Answer 1

$\bf \qquad \qquad \textit{Future Value of an ordinary annuity} \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]$


$\bf \qquad \begin{cases} A= \begin{array}{llll} \textit{original amount}\\ \textit{already compounded} \end{array}& \begin{array}{llll} \end{array}\\ pymnt=\textit{periodic payments}\to &200\\ r=rate\to 7\%\to \frac{7}{100}\to &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, four quarters} \end{array}\to &4\\ t=years\to &12 \end{cases} \\\\\\ A=200\left[ \cfrac{\left( 1+\frac{0.07}{4} \right)^{4\cdot 12}-1}{\frac{0.07}{4}} \right]$