Question

You borrowed $11,250 from the bank to buy a used car. You will pay the bank back

in 5 years with 3. 45% interest compounded annually. How much interest will you

end up paying?

A. $2,079. 23

B. $13,190. 63

C. $13,329. 23

D. $1,940. 63

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 &\$11250\\ r=rate\to 3.45\%\to (3.45)/(100)\dotfill &0.0345\\ 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=11250\left(1+(0.0345)/(1)\right)^(1\cdot 5) \implies A \approx 13329.23 ~\hfill \underset{interest~paid}{\stackrel{13329.23~~ - ~~11250}{\approx\text{\LARGE 2079.23}}}`