Question

1. aiden took out a mortgage on his home for $275,000 for 30 years at an annual interest rate of 4%. in january, alden paid $405 toward the principal and the rest of his mortgage payment was the interest on the loan. how much did alden pay in interest for the month of january? use the monthly mortgage payment table below.

	4%	5%	6%	7%
2 years	0.0434249	0.0438714	0.0443206	0.0447726
3 years	0.0295240	0.0299709	0.0304219	0.0308771
4 years	0.0225791	0.023093	0.0234850	0.0239462
5 years	0.0184165	0.0188712	0.0193328	0.0198012
15 years	0.0073969	0.0079079	0.0084386	0.0089883
20 years	0.0060598	0.0065996	0.00716543	0.0077530
25 years	0.0052874	0.0058459	0.0064430	0.0070678
30 years	0.0047742	0.0053682	0.0059955	0.0066530

• $750.00
• $817.91
• $859.92

Explanation:

Step1: Find monthly payment factor

For a 30 - year mortgage at 4% interest, the monthly payment factor from the table is 0.0047742.

Step2: Calculate total monthly payment

The total monthly payment (principal + interest) is calculated by multiplying the mortgage amount by the monthly payment factor. So, total monthly payment = $275,000\times0.0047742$.
\[275000\times0.0047742 = 275000\times\frac{47742}{10000000}=\frac{275000\times47742}{10000000}\]
\[275000\times47742 = 275000\times(40000 + 7000+700 + 40+2)=275000\times40000+275000\times7000 + 275000\times700+275000\times40+275000\times2\]
\[= 11000000000+1925000000+192500000 + 11000000+550000=11000000000 + 1925000000=12925000000+192500000 = 13117500000+11000000=13128500000+550000 = 13129050000\]
\[\frac{13129050000}{10000000}=1312.905\] (approx $1312.91$)

Step3: Calculate interest payment

We know that the total monthly payment is principal payment + interest payment. We are given that the principal payment is $495$. So, interest payment = total monthly payment - principal payment.
Interest payment=$1312.91 - 495=\$817.91$

Answer:

$\$817.91$