Question
Determine the simple interest earned on \( \$ 20,500 \) after 17 years if the APR is \( 10 \% \)
Ask by Lee Bowen. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simple interest earned is \$34,850.
Solution
To calculate the **simple interest** earned on an investment, you can use the following formula:
\[
\text{Simple Interest (I)} = P \times r \times t
\]
Where:
- \( P \) = Principal amount (\$20,500)
- \( r \) = Annual Interest Rate (as a decimal) (10% = 0.10)
- \( t \) = Time in years (17 years)
**Step-by-Step Calculation:**
1. **Convert the Annual Percentage Rate (APR) to a Decimal:**
\[
10\% = \frac{10}{100} = 0.10
\]
2. **Plug the Values into the Simple Interest Formula:**
\[
I = 20,500 \times 0.10 \times 17
\]
3. **Calculate the Interest:**
\[
I = 20,500 \times 0.10 = 2,050
\]
\[
I = 2,050 \times 17 = 34,850
\]
**Final Answer:**
The simple interest earned on \$20,500 after 17 years at an APR of 10% is **\$34,850**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To calculate simple interest, you can use the formula: \[ \text{Simple Interest} = P \times r \times t \] where \( P \) is the principal amount, \( r \) is the rate of interest per year, and \( t \) is the time in years. Here, \( P = \$20,500 \), \( r = 10\% = 0.10 \), and \( t = 17 \). Substituting the values in: \[ \text{Simple Interest} = 20,500 \times 0.10 \times 17 = 20,500 \times 1.7 = \$34,850 \] So, the simple interest earned after 17 years is \( \$34,850 \).
