Consider a student loan of $20,000 at a fixed fixed APR of 9% for 15 years. A. Claculate 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 $202.85.

B. The total amount paid over the term of the loan is $36,513.60.

C. The percentage paid toward the principal is 54.77%, while the percentage paid for interest is 45.23%.

Step-by-step explanation:

A. Calculate the monthly payment.

This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value or principal or student loan = $20,000

P = Monthly payment = ?

r = Monthly rate = APR /12 = 9% / 12 = 0.09 / 12 = 0.0075

n = number of months = 15 * 12 = 180

Substituting the values into equation (1) and solve for P, we have:

$20,000 = P * ((1 - (1 / (1 + 0.0075))^180) / 0.0075)

$20,000 = P * 98.5934088350577

P = $20,000 / 98.5934088350577 = $202.85

Therefore, the monthly payment is $202.85.

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

Total amount paid = Monthly payment * Number of months = $202.85 * 180 = $36,513.60

Therefore, the total amount paid over the term of the loan is $36,513.60.

C. Of the total amount paid what percentage is paid toward the principal and what percentage is paid for interest.

Percentage paid toward the principal = Principal / Total amount paid = $20,000 / $36,513.60 = 0.5477, or 54.77%

Percentage paid for interest = 100% - Percentage paid toward the principal = 100% - 54.77% = 45.23%

Therefore, the percentage paid toward the principal is 54.77%, while the percentage paid for interest is 45.23%.

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