A loan of $18,194 was repaid at the end of 17months. What size repayment check​ (principal and​ interest) was​ written, if an11.5% annual rate of interest was​ charged?

Question content area bottom Part 1The amount of the repayment check was enter your response here. ​(Round to two decimal​ places.)

To solve this problem, we will use the formula for the future value of a loan with simple interest:

\[
A = P \times \left( 1 + r \times t \right)
\]

Where:
- $ A $ = total amount repaid (principal + interest)
- $ P $ = principal (initial loan amount), which is $18,194
- $ r $ = annual interest rate (expressed as a decimal), which is 11.5% or 0.115
- $ t $ = time in years. Since the loan is repaid after 17 months, we convert that to years as $ t = \frac{17}{12} $.

### Step 1: Calculate $ t $ in years
\[
t = \frac{17}{12} \approx 1.4167 \, \text{years}
\]

### Step 2: Substitute the values into the formula
\[
A = 18,194 \times \left( 1 + 0.115 \times 1.4167 \right)
\]

### Step 3: Simplify the expression inside the parentheses
\[
A = 18,194 \times \left( 1 + 0.1639 \right)
\]
\[
A = 18,194 \times 1.1639
\]

### Step 4: Multiply to get the total repayment amount
\[
A \approx 18,194 \times 1.1639 \approx 21,168.27
\]

So, the amount of the repayment check is approximately **$21,168.27**.

Would you like further details or have any questions about the steps?

Here are 5 related questions you might consider:
1. How would the repayment change if the interest rate was 9.5%?
2. What if the loan period was 24 months instead of 17 months?
3. How would this calculation change if the interest were compounded monthly instead of simple interest?
4. What formula would apply if you wanted to know the monthly payment amount for a loan with monthly repayments?
5. How does the loan repayment change if the loan is paid earlier than the agreed period?

**Tip:** Always double-check the time conversion when working with months and years in interest calculations to avoid mistakes.

A loan of $18,194 was repaid at the end of 17 months. What size repayment check (principal and interest) was written, if an 11.5% annual rate of interest was charged? (Round to two decimal places.)

Learn how to calculate the repayment amount for a loan of $18,194 over 17 months with an 11.5% annual simple interest rate. Follow a step-by-step solution using the simple interest formula and time conversion. Suitable for high school students in Grades 10-12.

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