Question

a radio commercial for a loan company states: "you only pay for each $500 borrowed." If you borrow $1959 for 251 days, what amount will you repay, and what annual interest rate is the company actually charging? ( assume a 360- day year.)

Answer 1

Well... hmmm so.. for 500 bucks you only pay a rate of say "r", and it comes down to only 28cents, or $0.28.

If 500 is say the 100%, what percentage is 0.28?

$\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 500&100\\ 0.28&p \end{array}\implies \cfrac{500}{0.28}=\cfrac{100}{p}\implies p=\cfrac{0.28\cdot 100}{500} \\\\\\ p=0.056\%\implies p=\cfrac{56}{1000}\%$

now, we're assuming the company is charging and APR, so you pay that at the end of the year.  We're also assuming the year is only 360 days.

so, if you borrow 1959 on simple interest for 251 days out of 360 days, how much are you repaying?

$\bf \qquad \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \ 1959\\ r=rate\to 0.056\%\to \frac{0.056}{100}\to &0.00056\\ t=years\to &\frac{251}{360} \end{cases} \\\\\\ A=1959\left(1+0.00056\cdot \frac{251}{360} \right)$

and surely you can do that one... which is just 1959 and a few pennies.