Question

Your friend needs a loan of $4,800 for 8 months. You tell him for the simple interest loan service he needs to pay you back $4,944.00. What is the simple interest rate on your friendly loan? Round to the nearest tenth of percent, one decimal place in percent as needed.

Answer 1

the interest rate is 4.5%

Step-by-step explanation:

Amount of loan = $4800

duration of the laon = 8 months

Amount to pay back = $4944

Interest = amount to be paid back - initial amount of loan

Interest = 4944 - 4800

Interest = $144

Interest rate = ?

To get the interest rate (R), we will use the simple interest formula:

`\begin{gathered} I\text{ = PRT} \\ \text{where P = principal / loan} \\ R\text{ = rate} \\ T\text{ = time } \end{gathered}`
`\begin{gathered} P\text{ = 4800} \\ I\text{ = 144} \\ R\text{ = ?} \\ \text{T = 8 months = 8/12 year} \\ \\ \text{Substitute into the formula:} \\ 144\text{ = 4800 }*\text{ }R\text{ }*\text{ }(8)/(12) \end{gathered}`
`\begin{gathered} 144\text{ = 400 }*\text{ 8R} \\ 144\text{ = 3200R} \\ R\text{ = }(144)/(3200) \\ R\text{ = }(9)/(200)\text{ = 0.045} \\ \\ In\text{ percentage, R = 0.045 }*\text{ 100} \\ R\text{ = 4.5\%} \end{gathered}`

To the nearest tenth of a percent, the interest rate is 4.5%