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!