Question

HELP HELP HELP*. Hei has $1,700 in a retirement account earning 4% interest compounded annually. Each year after the first, she makes additional deposits of $1,700. After 5 years, what was her account balance if she did not make any withdrawals? Round each year's interest to the nearest cent if necessary.

what was account balance after 5 years

Answer 1

`~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}}\\ ~~~~~~~~~~~~ \\\\ A=pmt\left[ \cfrac{\left( 1+(r)/(n) \right)^(nt)-1}{(r)/(n)} \right]\left(1+(r)/(n)\right)`

`\begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill &1700\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=1700\left[ \cfrac{\left( 1+(0.04)/(1) \right)^(1\cdot 5)-1}{(0.04)/(1)} \right]\left(1+(0.04)/(1)\right) \\\\\\ A=1700\left( \cfrac{1.04^5~~ - ~~1}{0.04} \right)(1.04)\implies A\approx 9576.06`