Question

You take out a 60-day loan for $5000. At the end of the loan, you owe$73.97 in interest. What is the annual percentage rate? Round your answer to the nearest tenth of a percent.Rate = interest/principal x time

Answer 1

To solve this, we will apply the simple interest formula

`\begin{gathered} I=(PRT)/(100) \\ \text{where } \\ I=\text{the interest = }73.97 \\ P=\text{ the principal or money loaned = }$5000$\text{ dollars } \\ R=\text{ interest rate }=\text{ ?} \\ T=\text{ time in years = }(2)/(12) \\ \text{Note that 60 days is 2 months, so to change the month to year, we } \\ \text{divide by 12 } \end{gathered}`

Make R the subject we have

`\begin{gathered} I=(PRT)/(100) \\ \text{PRT = 100I} \\ \text{dividing by PT, we have } \\ (PRT)/(PT)=(100I)/(PT) \\ R=(100I)/(PT) \end{gathered}`

Substituting the values we have

`\begin{gathered} R=(100I)/(PT) \\ R=(100*73.97)/(5000*(2)/(12)) \\ R=(7397)/(833.333) \\ R=8.8764 \end{gathered}`

Hence the rate is 8.9% to the nearest tenth