Question

A car dealer will sell you a used car for $6,298 with $798 down and payments of $168.51 per month for 48 months. What is the simple interest rate? (Round your answer to the nearest tenth of a percent.)

Answer 1

so the car is regularly 6298 bucks, however the dealer will give it to you with 798 down and 168.51 for 48 months, so 48 payments of 168.51.

Now, the interest applies to the latter payments, not the downpayment, the downpayment is not financed, so it has no interest in it, since you're expected to slap the money down right there and then, grab your car and make the other payments... so hmmm

6298 - 798 = 5500

so after the downpayment you're only left to pay 5500, however the monthly payments add up to

168.51*14 = 8088.48

so there's a difference of 8088.48 - 5500 = 2588.48, and that happens over 48 months, so let's use that.

$~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \ 2588.48\\ P=\textit{original amount deposited}\dotfill & \ 5500\\ r=rate\to r\%\to \frac{r}{100}\\ t=months\dotfill &48 \end{cases} \\\\\\ 2588.48 = (5500)(\frac{r}{100})(48)\implies \cfrac{2588.48}{5500(48)}=\cfrac{r}{100}\implies \cfrac{8089}{825000}=\cfrac{r}{100} \\\\\\ \cfrac{808900}{825000}=r\implies \cfrac{8089}{8250}=r\implies \stackrel{\%}{1}\approx r$