Suppose you have student loans totaling $10,500 when you graduate from college. The APR is 9% and the loan term is 10 years.
a) What are your monthly payments?
b) What is the total amount you will pay over the term of the loan?
c) Of the total amount paid, what percentage is paid toward the principal?
d) Of the total amount paid, what percentage is paid for interest?
a)
P( 1 - (1+.09/12)^-120)/(.09/12) = 10500
P( 1 - 1.0075^-120)/.0075 = 10500
P = 133.01
b) - d) are actually bogus questions. Since you would be adding values of money that are not in the same "time spot" the result would be invalid.
The actual answer to "What is the total amount you will pay over the term of the loan?" would be " $10500 at 9% interest compounded monthly over 10 years"
but I will play the game:
133.01(120) = $15,961.15
so $5,961.15 would be interest and
$10500 would be principal
I will let you find the percentages.
To calculate the answers to these questions, we will need to use the formula for calculating monthly loan payments. The formula is:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate (APR divided by 12)
n = Total number of monthly payments (number of years multiplied by 12)
Now let's calculate the answers:
a) To calculate the monthly payments:
- Principal amount (P) = $10,500
- Annual interest rate (APR) = 9%
- Monthly interest rate (r) = APR / 12 = 0.09 / 12 = 0.0075
- Loan term (n) = 10 years = 10 * 12 = 120 months
Using the formula:
M = 10500 * (0.0075 * (1 + 0.0075)^120) / ((1 + 0.0075)^120 - 1)
M ≈ $137.38
So, your monthly payment will be approximately $137.38.
b) To calculate the total amount you will pay over the term of the loan:
- Monthly payment (M) = $137.38
- Loan term (n) = 120 months
Total amount paid = M * n
Total amount paid = $137.38 * 120
Total amount paid = $16,485.60
So, the total amount you will pay over the term of the loan is $16,485.60.
c) To calculate the percentage paid toward the principal:
- Total amount paid = $16,485.60
- Principal amount (P) = $10,500
Percentage paid toward the principal = (P / Total amount paid) * 100
Percentage paid toward the principal = ($10,500 / $16,485.60) * 100
Percentage paid toward the principal ≈ 63.75%
So, approximately 63.75% of the total amount paid is paid toward the principal.
d) To calculate the percentage paid for interest:
- Total amount paid = $16,485.60
- Principal amount (P) = $10,500
Percentage paid for interest = [(Total amount paid - P) / Total amount paid] * 100
Percentage paid for interest = [($16,485.60 - $10,500) / $16,485.60)] * 100
Percentage paid for interest ≈ 36.25%
So, approximately 36.25% of the total amount paid is paid for interest.