Consider a student loan of $$ \$ 25,000 $$ at a fixed APR of $$ 6 \% $$ 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. a. The monthly payment is $$ \$ \square $$. (Do not round until the final answer. Then round to the nearest cent as needed.)

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a. To calculate the monthly payment for a student loan, we can use the formula for the fixed monthly payment on a loan, which is:

$$ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} $$

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

Given:
- $$ P = \$25,000 $$
- The annual percentage rate (APR) is $$ 6\% $$, so the monthly interest rate $$ r $$ is $$ \frac{6\%}{12} = 0.005 $$.
- The term of the loan is 15 years, so the total number of payments $$ n $$ is $$ 15 \times 12 = 180 $$.

Now, let's plug in the values:

$$ M = 25000 \frac{0.005(1 + 0.005)^{180}}{(1 + 0.005)^{180} - 1} $$

Calculating this gives us:

$$ M = 25000 \frac{0.005(1.005)^{180}}{(1.005)^{180} - 1} $$

$$ M = 25000 \frac{0.005 \times 2.4134}{2.4134 - 1} $$

$$ M = 25000 \frac{0.012067}{1.4134} $$

$$ M = 25000 \times 0.008517 $$

$$ M = 212.425 $$

Rounded to the nearest cent, the monthly payment is $$ \$212.43 $$.

b. To determine the total amount paid over the term of the loan, we simply multiply the monthly payment by the total number of payments:

$$ \text{Total amount paid} = M \times n $$

$$ \text{Total amount paid} = 212.43 \times 180 $$

$$ \text{Total amount paid} = 38234.4 $$

Rounded to the nearest cent, the total amount paid over the term of the loan is $$ \$38,234.40 $$.

c. To find out what percentage of the total amount paid is paid toward the principal and what percentage is paid for interest, we can use the following formulas:

- Principal paid: $$ P = \text{Total amount paid} - \text{Total interest paid} $$
- Interest paid: $$ \text{Total interest paid} = \text{Total amount paid} - P $$

First, we need to calculate the total interest paid:

$$ \text{Total interest paid} = M \times n - P $$

$$ \text{Total interest paid} = 212.43 \times 180 - 25000 $$

$$ \text{Total interest paid} = 38234.4 - 25000 $$

$$ \text{Total interest paid} = 13234.4 $$

Now, we can calculate the percentage paid toward the principal and the percentage paid for interest:

- Percentage paid toward the principal:

$$ \text{Percentage paid toward principal} = \frac{P}{\text{Total amount paid}} \times 100 $$

$$ \text{Percentage paid toward principal} = \frac{25000}{38234.4} \times 100 $$

$$ \text{Percentage paid toward principal} \approx 65.23\% $$

- Percentage paid for interest:

$$ \text{Percentage paid for interest} = \frac{\text{Total interest paid}}{\text{Total amount paid}} \times 100 $$

$$ \text{Percentage paid for interest} = \frac{13234.4}{38234.4} \times 100 $$

$$ \text{Percentage paid for interest} \approx 34.77\% $$

So, approximately $$ 65.23\% $$ of the total amount paid is paid toward the principal, and approximately $$ 34.77\% $$ is paid for interest.
a. The monthly payment is $$ \$212.43 $$. b. The total amount paid over the term of the loan is $$ \$38,234.40 $$. c. Approximately $$ 65.23\% $$ is paid toward the principal, and approximately $$ 34.77\% $$ is paid for interest.

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