Question

You take out a car loan for $7,300 at an interest rate of 4.2% for a duration of 5 years

compounded quarterly. What is the total amount that you will pay back to the bank?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7300\\ r=rate\to 4.2\%\to (4.2)/(100)\dotfill &0.042\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A=7300\left(1+(0.042)/(4)\right)^(4\cdot 5)\implies A=7300(1.0105)^(20)\implies A\approx 8996`