Question

According to the formula, if the end of year deposit is $1,777.31, the annual interest rate is 5%, and the term is 18 years, find A.
A. $41,088.42 B. $50,000.00 C. $50,968.22 D. $53,920.75

Answer 1

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

$\bf ~~~~~~ \begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array}\to & \begin{array}{llll} \end{array}\\ pymnt=\textit{periodic payments}\to &1777.31\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{is done on a yearly basis} \end{array}\to &1\\ t=years\to &18 \end{cases}$

$\bf A=1777.31\left[ \cfrac{\left( 1+\frac{0.05}{1} \right)^{1\cdot 18}-1}{\frac{0.05}{1}} \right]\implies A=1777.31\left( \cfrac{1.05^{18}}{0.05} \right)$