Answer:
A. 694.79 per month
B. 208,437 total repaid
C. 60% to principal; 40% to interest
Step-by-step explanation:
You want to know the monthly payment, the total repaid, and the fractions that go to principal and interest for a 25-year loan of 125000 at 4.5%.
A. Payment
The amount of the monthly payment is given by the amortization formula:
[tex]A=\dfrac{P\left(\dfrac{r}{12}\right)}{1-\left(1+\dfrac{r}{12}\right)^{-12t}}[/tex]
where P is the loan amount at rate r for t years.
Using the given values, we find the monthly payment to be ...
[tex]A=\dfrac{125000\left(\dfrac{0.045}{12}\right)}{1-\left(1+\dfrac{0.045}{12}\right)^{-12(25)}}\approx694.79[/tex]
The monthly payment is 694.79.
B. Total paid
The total value of the 300 payments of 694.79 is ...
total paid = 300×694.79 = 208,437
The total amount paid over 25 years is 208,437.
C. Percent to principal
The fraction of the amount paid that goes to principal is ...
% to P = 125,000/208,437 × 100% ≈ 60.0%
The remaining amount is paid for interest: 100% -60.0% = 40.0%
Of the amount paid, 60.0% is paid toward principal; 40.0% is paid for interest.
