To calculate the monthly payment on the loan, we need to follow these steps:

Step 1: Understand the Loan Details

• Loan Amount ($P$) = $7500
• Annual Interest Rate ($r$) = 6.3% or 0.063
• Loan Term = 10 years
• Deferment Period = 6 months after graduation

Step 2: Calculate the Loan Balance at the Time Payments Begin

Since the student graduates 3 years and 9 months after the loan is acquired, there will be a deferment period of 6 months after graduation. Therefore, we need to calculate how much interest accrues over this total period (3 years and 9 months + 6 months of deferment).

The total deferment time is: $3 \text{ years } 9 \text{ months} + 6 \text{ months} = 4 \text{ years } 3 \text{ months} = 4.25 \text{ years}$

The formula for the accumulated loan balance at the end of the deferment period (before payments start) is: $A = P(1 + r)^{t}$ Where:

• $A$ is the amount owed after deferment
• $P$ is the principal amount ($7500)
• $r$ is the annual interest rate (0.063)
• $t$ is the deferment period in years (4.25 years)

Now, let's compute the accumulated amount.

Step 3: Calculate the Monthly Payment Using the Loan Amortization Formula

Once we have the balance after deferment, we use the following formula to calculate the monthly payment:

$M = \frac{A \cdot r_{\text{monthly}}}{1 - (1 + r_{\text{monthly}})^{-n}}$ Where:

• $M$ is the monthly payment
• $A$ is the accumulated loan balance
• $r_{\text{monthly}}$ is the monthly interest rate, which is $\frac{r}{12}$
• $n$ is the number of months in the loan term (10 years = 120 months)

I'll now calculate the balance after deferment and then the monthly payment. Given data P = 7500 # Principal loan amount in dollars annual_interest_rate = 0.063 # Annual interest rate t_deferment = 4.25 # Deferment period in years (3 years 9 months + 6 months)

Monthly interest rate

r_monthly = annual_interest_rate / 12

Calculating the amount owed after deferment

A = P * (1 + annual_interest_rate) ** t_deferment

Loan term in months (10 years)

loan_term_months = 10 * 12

Calculating the monthly payment using the amortization formula

M = (A * r_monthly) / (1 - (1 + r_monthly) ** -loan_term_months)

A, MAfter the deferment period of 4.25 years, the loan balance will be approximately $9723.61.

The monthly payment on the loan, starting after the 6-month deferment period, will be $109.42.

Would you like more details or have any questions?

Related questions:

1. How do you calculate the loan balance after a deferment period?
2. What is the impact of deferment on loan interest accrual?
3. How do you compute the total amount paid over the life of the loan?
4. What are the differences between deferment and forbearance for student loans?
5. How can early repayment affect the total interest paid on a loan?

Tip: Always check for any grace period after deferment, as it can affect the start of your first payment!