Question

$100 is deposited at the end of every week for five years in an account that pays 14%/an, compounded weekly. (8) What type of annuity is this? Find the future value of the annuity using the formula. Find the future value of the annuity using a spreadsheet. In your answer include the formulas that you typed. Find the future value of the annuity using the TVM solver on a graphing calculator or on a website. In your answer, include what values you typed for each parameter.

Answer 1

Annuities whose payments are made at the end of the period are "ordinary annuity" type

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

$\bf \qquad \begin{cases} A= \begin{array}{llll} \textit{accumulated amount} \end{array} \\ pymnt=\textit{periodic payments}\to &100\\ r=rate\to 14\%\to \frac{14}{100}\to &0.14\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus} \end{array}\to &52\\ t=years\to &5 \end{cases} \\\\\\ A=100\left[ \cfrac{\left( 1+\frac{0.14}{52} \right)^{52\cdot 5}-1}{\frac{0.14}{52}} \right]$