Question

The simple interest charged on a 65 day loan of $1250 is $7.75. Find the annual simple interest rate in precent for this loan round to the nearest tenth of a percent. Use 360 days in 1 year

Answer 1

We have a loan of 65 days.

The principal is $1250 and the interest is $7.75.

We have to find the annual simple interest rate.

We can express the interest of a loan of this type as:

`I=r\cdot(t)/(360)\cdot P`

where r = annual interest rate, t = period of the loan in days, I = interest and P = principal.

Then, we can rearrange the equation and replace with the values:

`\begin{gathered} I=r\cdot(t)/(360)\cdot P \\ r=(I\cdot360)/(t\cdot P) \\ r=(7.75\cdot360)/(65\cdot1250) \\ r=(2790)/(81250) \\ r\approx0.03433846 \\ r\approx3.4\% \end{gathered}`

Answer: the annual simple interest rate is 3.4%.