Question

Consider a student loan of ​$17,500 at a fixed APR of 6​% for 3 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.

Answer 1

To find the monthly payment use the formula of the present value of an annuity ordinary which is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv student loan 17500
PMT monthly payment?
R interest rate 0.06
K compounded monthly 12 because the payments are monthly.
N time 3 years
Solve the formula for PMT to get
PMT=pv÷[(1-(1+r/k)^(-kn))÷(r/k)]
PMT=17,500÷((1−(1+0.06÷12)^(
−12×3))÷(0.06÷12))
=532.38

The total amount paid
532.38×12months×3 years
=19,165.68

The percentage is paid toward the principal is
(17,500÷19,165.68)×100
=91.31%

The percentage is paid for interest is
((19,165.68−17,500)÷19,165.68)×100
=8.69%

Hope it helps!