Mackenzie received a 4.75% nonsubsidized 15-year student loan for $24,000. Assuming she graduates in 4 years, determine Mackenzie's monthly payment on the loan.

To determine Mackenzie's monthly payment on her student loan, we will use the **amortization formula**, which calculates the fixed monthly payments for a loan. The formula is:

\[
M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- $M$ is the monthly payment,
- $P$ is the loan amount (principal),
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the total number of payments (loan term in months).

### Step 1: Identify the known values.
- **Loan Amount (P):** $24,000
- **Annual Interest Rate:** 4.75% (or 0.0475 in decimal)
- **Loan Term:** 15 years = $ 15 \times 12 = 180 $ months

### Step 2: Calculate the monthly interest rate.
\[
r = \frac{0.0475}{12} = 0.0039583
\]

### Step 3: Calculate the total number of payments.
Since Mackenzie graduates in 4 years, she will have 11 years (remaining from the 15-year term) to repay the loan after graduation.
\[
n = 11 \times 12 = 132 \text{ months}
\]

### Step 4: Plug the values into the amortization formula.
\[
M = \frac{24000 \cdot 0.0039583 \cdot (1 + 0.0039583)^{132}}{(1 + 0.0039583)^{132} - 1}
\]

### Step 5: Solve for $M$.
After computing the formula, Mackenzie's **monthly payment** comes out to approximately **$229.17**.

This is the amount she would need to pay monthly to repay the loan over 11 years, starting after graduation.

Would you like a more detailed breakdown of these steps or have any further questions?

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Here are 5 related questions:
1. What would happen if the interest rate increased to 6%?
2. How does the loan term affect the monthly payment?
3. How would her monthly payment change if she paid off the loan in 10 years?
4. What if Mackenzie made extra payments during the first 4 years of school?
5. How would her payments change if she had a subsidized loan?

**Tip:** Making extra payments early reduces the principal, helping to save on interest over time.

Mackenzie received a 4.75% nonsubsidized 15-year student loan for $24,000. Assuming she graduates in 4 years, determine Mackenzie's monthly payment on the loan.

Learn how to calculate the monthly payment for a $24,000 nonsubsidized student loan with a 4.75% interest rate over an 11-year repayment period. This example covers the amortization formula and interest rate concepts, ideal for students studying financial mathematics or personal finance.

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