Consider a student loan of ​$20 comma 000 at a fixed APR of 9​% for 20 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.  (Do not round until the final answer. Then round to the nearest cent as​ needed.)

This is a problem about a fixed-rate loan, where we calculate the monthly payment, the total amount paid over the loan term, and determine the breakdown between principal and interest.

We will use the loan amortization formula to solve this. The formula for the monthly payment $ M $ is:

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

Where:
- $ P $ is the loan principal (\$20,000),
- $ r $ is the monthly interest rate (annual rate divided by 12),
- $ n $ is the total number of payments (loan term in years multiplied by 12).

### Step 1: Calculate the Monthly Payment

Given:
- Principal $ P = 20,000 $ USD,
- Annual Interest Rate (APR) = 9% → monthly interest rate $ r = \frac{9\%}{12} = 0.0075 $,
- Loan term $ n = 20 \times 12 = 240 $ months.

Now, we can plug in the values and calculate the monthly payment.

\[
M = 20,000 \times \frac{0.0075(1 + 0.0075)^{240}}{(1 + 0.0075)^{240} - 1}
\]

I'll compute the exact value.The monthly payment is approximately \$179.95.

### Step 2: Calculate the Total Amount Paid Over the Term of the Loan
The total amount paid over the life of the loan is the monthly payment multiplied by the total number of payments:

\[
\text{Total amount paid} = M \times n
\]

Let's calculate that now.The total amount paid over the term of the loan is approximately \$43,186.85.

### Step 3: Determine the Percentage Paid Toward the Principal and Interest
To find the amounts paid toward the principal and interest:

- The amount paid toward the principal is simply the loan amount: $ P = 20,000 $ USD.
- The amount paid toward interest is the difference between the total amount paid and the principal:

\[
\text{Interest paid} = \text{Total amount paid} - \text{Principal}
\]

Next, calculate the percentage breakdown:
- Percentage paid toward principal:
\[
\frac{\text{Principal}}{\text{Total amount paid}} \times 100
\]
- Percentage paid toward interest:
\[
\frac{\text{Interest paid}}{\text{Total amount paid}} \times 100
\]

Let's compute these values.The breakdown of the total amount paid is as follows:

- Interest paid: \$23,186.85
- Percentage of total payment toward principal: approximately 46.31%
- Percentage of total payment toward interest: approximately 53.69%

Would you like any further details or have questions?

Here are 5 related questions to expand on this:
1. How would the monthly payment change if the APR was reduced to 7%?
2. How much interest would be saved if the loan was paid off in 15 years instead of 20?
3. What if the loan amount was increased to \$30,000 with the same APR and term?
4. How does the loan amortization schedule change with varying payment amounts?
5. What are the benefits of making extra payments on a loan with a fixed APR?

**Tip:** Making additional payments on your loan can significantly reduce the total interest paid over the loan's term.

Consider a student loan of $20,000 at a fixed APR of 9% for 20 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. (Do not round until the final answer. Then round to the nearest cent as needed.)

Learn how to calculate the monthly payment, total amount paid, and the percentage of principal and interest on a $20,000 student loan with a 9% APR over 20 years. This problem covers key concepts in loan amortization and interest rate calculations, suitable for college or advanced high school students.

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