I am having problems with this question in my math class.

Consider a student loan of ​$25,000.00 at a fixed APR of 12% for 25 years.

a. Calculate the monthly payment. The monthly payment is $263.31
b. Determine the total amount paid over the term of the loan. This is $78,993.00
c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.
I am not sure how to figure out the percentage paid toward the principal and what percentage is paid for interest.

I agree with your first two answers.

The third question makes no "actuarial mathematical" sense.
The closest I would guess is :
78,993.00 - 25000 = 53993
rate = interest/(principal x time) = 53993/(25000(25)) = .0863
so 8.63 % ??

I got the question wrong so they gave me the answer and I have another chance to answer a similiar question. The percentage toward the principal is 31.6, toward interest it is 68.4. I can't figure out how they got the percentages.

This is my new question
Consider a student loan of ​$22,500.00 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.

I see what they did.

percentage interest = interest/total paid
= 53993/78,993 = .6835...
or appr 68.4%
so the principal percentage = 100%-68.4% = 31.6%

What formula were you using to get the first two answers?
Hint: This is a "present value of an annuity" type of question.

Thank you so much. I went online and I did it with an online calculator. I have been out of school for 15 years and the formulas confuse me so much.

Thank you again for your help. I now know how to do these problems and I got the other one right. I may have many more questions.


Thank you,
Stephanie

yes

To determine the percentage paid toward the principal and the percentage paid for interest, we need to understand how loan payments are typically structured.

Each monthly payment consists of two parts: principal and interest. The principal is the original loan amount, and the interest is the cost of borrowing the money.

Here's how you can calculate the percentages:

Step 1: Calculate the total interest paid over the term of the loan.
To find the total interest, multiply the monthly payment by the number of payments made over the loan term, and subtract the original loan amount.

Total Interest = (Monthly Payment) x (Total Number of Payments) - (Original Loan Amount)

In this case:
Total Interest = ($263.31) x (25 years x 12 months/year) - ($25,000.00)

Step 2: Calculate the percentage of the total amount paid towards interest.
Divide the total interest by the total amount paid over the term of the loan, and multiply the result by 100 to convert it into a percentage.

Percentage of Interest = (Total Interest / Total Amount Paid) x 100

Total Amount Paid = Total Interest + Original Loan Amount (since the monthly payment consists of principal + interest)

Step 3: Calculate the percentage of the total amount paid towards the principal.
Divide the original loan amount by the total amount paid over the term of the loan, and multiply the result by 100 to convert it into a percentage.

Percentage of Principal = (Original Loan Amount / Total Amount Paid) x 100

Now that you have all the necessary formulas, substitute the given values into the equations to find the desired percentages.