To solve this problem, we will follow these steps:

Step 1: Understand the Problem

• Loan amount (Principal): $8,500
• Annual interest rate: 6.3%
• Time before payments start: 2 years and 7 months (until graduation) + 6 months of deferment = 3 years and 1 month = 37 months

Step 2: Convert the Annual Interest Rate to a Monthly Interest Rate

The annual interest rate is given as 6.3%. To find the monthly interest rate, we divide the annual interest rate by 12: $\text{Monthly interest rate} = \frac{6.3\%}{12} = 0.525\%$ This is 0.525% per month, or as a decimal: $\text{Monthly interest rate (decimal)} = \frac{0.525}{100} = 0.00525$

Step 3: Find the Interest Accrued in a 30-Day Month

To calculate the interest that accrues in one month, use the formula for simple interest: $\text{Interest per month} = P \times r$ where $P$ is the principal and $r$ is the monthly interest rate.

For the first month: $\text{Interest for one month} = 8,500 \times 0.00525 = 44.625$ So, $44.63 accrues as interest each month.

Step 4: Find the Total Interest Accrued Before Regular Payments Begin

The time period before payments begin is 37 months. The interest is compounded monthly (meaning each month interest is added to the total), so we can use the simple accumulation formula to find the total interest accrued over 37 months.

The formula for simple monthly interest is: $\text{Total interest} = P \times r \times t$ where $t$ is the number of months.

For this loan: $\text{Total interest} = 8,500 \times 0.00525 \times 37 = 1,651.125$ Thus, the total interest accrued before payments begin is $1,651.13.

Final Answer:

• The interest that accrues in a 30-day month is $44.63.
• The total amount of interest that accrues over the 37 months before regular payments begin is $1,651.13.

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Would you like further details or have any questions? Here are some related questions you could consider:

1. How would the calculation change if the interest rate were different?
2. What would the total interest be if the deferment period was reduced to 3 months?
3. How does compound interest affect loan repayment in the long term?
4. What would the monthly payment be once payments start?
5. What are some strategies to pay off student loans faster?

Tip: If you can make small interest-only payments during deferment, you can reduce the amount of interest that accumulates over time!