Village Finance Co. advanced three loans to Kamiko—$2200 on June 23, $1800 on August 5 ,and $1300 on October 31. Simple interest at 7.25% was charged on all three loans, and all were repaid on December 31 when some bonds that she owned matured. What total amount was required to pay off the loans?

To find the total amount required to pay off Kamiko's loans, we need to calculate the simple interest for each loan and then add it to the principal amounts. Simple interest is calculated using the formula:

\[
I = P \times r \times t
\]
Where:
- $ I $ = interest
- $ P $ = principal (amount of the loan)
- $ r $ = annual interest rate (as a decimal)
- $ t $ = time period (in years)

The loans were repaid on December 31, so we need to calculate the time period $ t $ in years for each loan.

### Loan 1: $2200 on June 23
- Time period: From June 23 to December 31
  - This is 6 months and 8 days, or approximately $ t = \frac{191}{365} \approx 0.523 $ years.
- Interest rate: $ r = 7.25\% = 0.0725 $
- Principal: $ P = 2200 $

\[
I_1 = 2200 \times 0.0725 \times 0.523 = 83.21
\]

### Loan 2: $1800 on August 5
- Time period: From August 5 to December 31
  - This is 4 months and 26 days, or approximately $ t = \frac{148}{365} \approx 0.405 $ years.
- Principal: $ P = 1800 $

\[
I_2 = 1800 \times 0.0725 \times 0.405 = 52.91
\]

### Loan 3: $1300 on October 31
- Time period: From October 31 to December 31
  - This is 2 months, or approximately $ t = \frac{61}{365} \approx 0.167 $ years.
- Principal: $ P = 1300 $

\[
I_3 = 1300 \times 0.0725 \times 0.167 = 15.74
\]

### Total Interest
\[
\text{Total Interest} = I_1 + I_2 + I_3 = 83.21 + 52.91 + 15.74 = 151.86
\]

### Total Amount to Pay Off
To pay off the loans, Kamiko must pay the total principal plus the total interest.

\[
\text{Total Amount} = 2200 + 1800 + 1300 + 151.86 = 5451.86
\]

Thus, the total amount required to pay off the loans is **$5451.86**.

Would you like more details or have any questions about this?

Here are 5 related questions:
1. How would the total amount change if the interest rate were 8% instead of 7.25%?
2. What would happen if Kamiko repaid the loans on November 30 instead of December 31?
3. How is simple interest different from compound interest in this scenario?
4. How much interest would be saved if the loans were repaid 1 month earlier?
5. How do the different time periods affect the overall interest in the loans?

**Tip:** When dealing with simple interest, always make sure to convert the time period to years, as the interest rate is typically given on an annual basis.

Village Finance Co. advanced three loans to Kamiko—$2200 on June 23, $1800 on August 5, and $1300 on October 31. Simple interest at 7.25% was charged on all three loans, and all were repaid on December 31 when some bonds that she owned matured. What total amount was required to pay off the loans?

Learn how to calculate the total amount required to repay three loans with a 7.25% interest rate, including detailed steps to find the simple interest for each loan based on different time periods. Suitable for Grades 9-12 math students.

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