A loan of $ 11 comma 874 was repaid at the end of 9 months. What size repayment check​ (principal and​ interest) was​ written, if a 7.3 % annual rate of interest was​ charged?
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Part 1
The amount of the repayment check was ​$
  
enter your response here. ​(Round to two decimal​ places.)

To calculate the amount of the repayment check (which includes both principal and interest), we can use the formula for simple interest:

\[
A = P \left( 1 + \frac{r \cdot t}{100} \right)
\]

Where:
- $ A $ is the total amount (principal + interest),
- $ P $ is the principal (the original loan amount),
- $ r $ is the annual interest rate (in percentage),
- $ t $ is the time in years.

Given:
- $ P = 11,874 $,
- $ r = 7.3\% $,
- $ t = 9 \text{ months} = \frac{9}{12} \text{ years} = 0.75 \text{ years}. $

Now, plug the values into the formula:

\[
A = 11,874 \left( 1 + \frac{7.3 \cdot 0.75}{100} \right)
\]

First, calculate the interest factor:

\[
\frac{7.3 \cdot 0.75}{100} = \frac{5.475}{100} = 0.05475
\]

Then:

\[
A = 11,874 \left( 1 + 0.05475 \right) = 11,874 \times 1.05475 = 12,526.23
\]

So, the repayment check amount is **$12,526.23**.

Would you like more details on this? 

Here are five related questions:
1. How would the repayment change if the interest rate were compounded monthly instead of simple?
2. What would the repayment be if the interest rate increased to 8%?
3. How does the time period affect the interest calculation for loans?
4. What happens to the repayment if the loan is repaid after 6 months instead of 9 months?
5. What is the total interest paid in this loan?

**Tip**: Always ensure the time in the interest formula matches the unit used for the rate (annual rate = time in years).

A loan of $11,874 was repaid at the end of 9 months. What size repayment check (principal and interest) was written, if a 7.3% annual rate of interest was charged?

Learn how to calculate the loan repayment amount of $11,874 after 9 months at a 7.3% annual interest rate. This step-by-step guide covers the use of the simple interest formula to find the repayment check of $12,526.23.

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