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

SOLUTION

To solve this, we will apply the simple interest formula

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

Make R the subject we have

$\begin{gathered} I=\frac{PRT}{100} \\ \text{PRT = 100I} \\ \text{dividing by PT, we have } \\ \frac{PRT}{PT}=\frac{100I}{PT} \\ R=\frac{100I}{PT} \end{gathered}$

Substituting the values we have

$\begin{gathered} R=\frac{100I}{PT} \\ R=\frac{100\times73.97}{5000\times\frac{2}{12}} \\ R=\frac{7397}{833.333} \\ R=8.8764 \end{gathered}$

Hence the rate is 8.9% to the nearest tenth