Assume you graduate from university with a $35,000 student loan. If your interest rate is fixed at 5.21% APR with monthly compounding and you will repay the loan over a 10​-year ​period, what will be your monthly​ payment?

To determine your monthly payment for the student loan, we can use the formula for the monthly payment on an amortizing loan:

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

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

### Given:
- $ P = 35,000 $ (loan amount),
- APR = 5.21% (annual percentage rate),
- Loan term = 10 years.

First, we need to convert the annual interest rate to a monthly interest rate:
\[
r = \frac{5.21\%}{12} = \frac{0.0521}{12} = 0.004342 \, \text{(monthly interest rate)}.
\]

Next, we calculate the total number of payments over 10 years (120 months):
\[
n = 10 \times 12 = 120.
\]

Now, substituting these values into the formula for the monthly payment:
\[
M = \frac{35,000 \times 0.004342 \times (1 + 0.004342)^{120}}{(1 + 0.004342)^{120} - 1}.
\]

Now let's calculate the result:

\[
M \approx \frac{35,000 \times 0.004342 \times (1.004342)^{120}}{(1.004342)^{120} - 1}.
\]

Calculating the powers and final values:

\[
M \approx \frac{35,000 \times 0.004342 \times 1.682024}{1.682024 - 1}.
\]
\[
M \approx \frac{35,000 \times 0.004342 \times 1.682024}{0.682024}.
\]
\[
M \approx \frac{256.47 \times 1.682024}{0.682024}.
\]
\[
M \approx 631.70.
\]

### Final Monthly Payment:
Your monthly payment will be approximately **$631.70**.

Would you like more details or have any questions?

### Related Questions:
1. How is the total interest paid over the loan term calculated?
2. What happens if you make additional payments?
3. How do changes in APR affect monthly payments for student loans?
4. What is the impact of extending the loan term?
5. What is the formula for an amortization schedule for this loan?

**Tip:** Making additional payments early on can help reduce the total interest you pay over the loan's life.

Assume you graduate from university with a $35,000 student loan. If your interest rate is fixed at 5.21% APR with monthly compounding and you will repay the loan over a 10-year period, what will be your monthly payment?

Learn how to calculate the monthly payment for a $35,000 student loan with a 5.21% APR over 10 years, using the amortization formula. This solution explains compounding interest, loan terms, and how to determine the fixed monthly payments. Suitable for Grades 10-12 and early college students.

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