Consider a student loan of

​$15 comma 00015,000

at a fixed APR of

1212​%

for

1515

years.

a. Calculate the monthly payment.

b. Determine the total amount paid over the term of the loan.

c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.

Question content area bottom

Part 1

a. The monthly payment is

​$enter your response here.

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

To solve this, we can use the formula for calculating monthly payments on a fixed-rate loan, which is:

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

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

### Given dataTo solve this, we can use the formula for calculating monthly payments on a fixed-rate loan, which is:

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

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

### Given 
- Loan amount ($P$) = \$15,000
- Annual percentage rate (APR) = 12%
- Loan term = 15 years

#### Step 1: Convert the APR to the monthly interest rate
\[
r = \frac{12\%}{12} = 0.01 \, \text{(monthly interest rate)}
\]

#### Step 2: Determine the number of payments
\[
n = 15 \times 12 = 180 \, \text{(monthly payments over 15 years)}
\]

#### Step 3: Plug values into the monthly payment formula

\[
M = 15000 \times \frac{0.01(1 + 0.01)^{180}}{(1 + 0.01)^{180} - 1}
\]

Let me calculate this for you.The monthly payment is approximately \$180.03.

Next steps:
- **b.** To calculate the total amount paid over the term of the loan, multiply the monthly payment by the number of payments ($ n = 180 $).
- **c.** To find out what percentage is paid toward the principal and what percentage is paid toward interest, we need to calculate the total interest paid.

Would you like me to continue with parts b and c?

Here are 5 related questions for deeper understanding:
1. How does the loan term affect the monthly payment?
2. What happens to the monthly payment if the interest rate changes?
3. How does an increase in the loan amount affect the total interest paid?
4. What is the impact of making additional payments on the principal balance?
5. How is the amortization schedule for this loan structured?

**Tip:** When dealing with loans, small changes in the interest rate or loan term can significantly impact the total interest paid.

Consider a student loan of $15,000 at a fixed APR of 12% for 15 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

Learn how to calculate the monthly payment for a $15,000 student loan with a 12% fixed APR over 15 years. This problem demonstrates the use of loan amortization formulas, interest rate calculations, and basic algebra. Includes a step-by-step solution and explanations.

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