Respuesta :
Answer:
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%.
