Question
Use a formula to solve the problem. To start a mobile dog-grooming service, a woman borrowed \( \$ 2,500 \). If the loan was for 2 years and the amount of interest was \( \$ 240 \), what simple interest rate was she charged? SUBMIT ANSWER
Ask by Mullins Herrera. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simple interest rate was 4.8%.
Solution
We start with the formula for simple interest:
\[
I = P \times r \times t
\]
where
- \( I \) is the interest,
- \( P \) is the principal,
- \( r \) is the rate, and
- \( t \) is the time.
Given:
- \( I = \$240 \),
- \( P = \$2500 \),
- \( t = 2 \) years.
Plug these values into the formula:
\[
240 = 2500 \times r \times 2
\]
Simplify the right side:
\[
240 = 5000 \times r
\]
Solve for \( r \):
\[
r = \frac{240}{5000}
\]
\[
r = 0.048
\]
To convert the decimal to a percentage, multiply by 100:
\[
r = 0.048 \times 100 = 4.8\%
\]
Thus, the simple interest rate was \( 4.8\% \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To find the simple interest rate, you can use the formula: \[ I = P \times r \times t \] where \( I \) is the interest earned, \( P \) is the principal amount (the initial loan), \( r \) is the interest rate (in decimal form), and \( t \) is the time in years. We need to isolate \( r \): \[ r = \frac{I}{P \times t} \] Plugging in the values: \[ I = 240, \quad P = 2500, \quad t = 2 \] Now, substituting these into the formula: \[ r = \frac{240}{2500 \times 2} = \frac{240}{5000} = 0.048 \] To convert the decimal to a percentage, multiply by 100: \[ r = 0.048 \times 100 = 4.8\% \] So, the simple interest rate charged was **4.8%**.
