For the given student loan, find the interest that accrues in a 30-day month, then find the total amount of interest that will accrue before regular payments begin, again using 30-day months.

$6400 at 6.5% interest; student graduates 2 years and 6 months after loan is acquired; payments deferred for 6 months after graduation.

The interest that accrues in a 30-day month is $_. Round to two decimal places, if necessary.

### Step 1: Calculate the interest accrued in a 30-day month.

To calculate the monthly interest accrued on a loan, we use the following formula:

\[
\text{Interest for 30 days} = \left(\frac{r}{n}\right) \times P
\]

Where:
- $ P $ is the principal (the loan amount).
- $ r $ is the annual interest rate (in decimal form).
- $ n $ is the number of periods in a year (since we are using 30-day months, $ n = 12 $).

For this problem:
- $ P = 6400 $ (the loan amount).
- $ r = 6.5\% = 0.065 $.
- $ n = 12 $ months.

\[
\text{Interest for 30 days} = \left(\frac{0.065}{12}\right) \times 6400
\]

Let's calculate the result.The interest that accrues in a 30-day month is approximately \$34.67.

### Step 2: Calculate the total interest accrued before regular payments begin.

The student graduates 2 years and 6 months after acquiring the loan, and payments are deferred for 6 months after graduation. Therefore, the total time before payments begin is:

\[
2.5 \text{ years} + 0.5 \text{ years} = 3 \text{ years} = 36 \text{ months}
\]

The total interest accrued during this time is:

\[
\text{Total interest} = \text{Interest per month} \times \text{Number of months}
\]

\[
\text{Total interest} = 34.67 \times 36
\]

Let me calculate that for you.The total amount of interest that will accrue before regular payments begin is approximately \$1248.00.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the accrued interest change if the interest rate was 7%?
2. What if payments were deferred for only 3 months instead of 6?
3. How would the interest be affected if the principal was $7,500 instead of $6,400?
4. What is the total loan amount (principal + accrued interest) at the start of repayment?
5. How does the length of the deferment period affect the total accrued interest?

**Tip:** The earlier you begin making payments on a loan, the less interest will accumulate. Consider paying during deferment if possible!

For the given student loan, find the interest that accrues in a 30-day month, then find the total amount of interest that will accrue before regular payments begin, again using 30-day months.

$6400 at 6.5% interest; student graduates 2 years and 6 months after loan is acquired; payments deferred for 6 months after graduation.

Find out how to calculate the interest that accrues on a $6400 student loan at 6.5% interest over a 30-day month, along with the total interest accrued before payments start after a deferment period. This problem involves key concepts of interest calculation and loan deferment, ideal for students in Grades 10-12.

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