Question

Lance Rice has decided to invest $1,200 quarterly for eight years in an ordinary annuity at 4%. The total cash value of the annuity at end of year 8 is

Answer 1

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

$\bf \begin{cases} A= \begin{array}{llll} \textit{original amount}\\ \textit{already compounded} \end{array}\begin{array}{llll}\end{array}\\ pymnt=\textit{periodic payments}\to &1200\\ r=rate\to 4\%\to \frac{4}{100}\to &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, meaning } \end{array}\to &4\\ t=years\to &8 \end{cases} \\\\\\ A=1200\left[ \cfrac{\left( 1+\frac{0.04}{4} \right)^{4\cdot 8}-1}{\frac{0.04}{4}} \right]$