Question

The following information is for the next five questions:

Ryan and Laurie Middleton just purchased their first home with a traditional (monthly compounding and payments) 6% 30-year mortgage loan of $150,000.

What is their monthly payment?

		$5,96.84
		$899.33
		$9,000
		$419.80

What is their interest payment during the first year?

What is their principal payment during the first year?

What is their interest payment during the 25th year?

What is their principal payment during the 25th year?

Answer 1

Given

A )

Loan Amount P=$150,000

rate =6%

Monthly rate r=6%/12=0.5%

Period of loan N=30*12=360

So Payment per month A=P*r/(1-(1+r)^-N)

A=150000*0.5%/(1-(1+0.5%)^-360)

A=$899.33

B)

Total Payment made during 1st year =12*899.33=$10791.96

Balanced principle amount after 1st year payment =899.33*(1-(1+0.5%)^-348)/0.5%=$148,157.98

So Interest paid during 1st year =Total Payment made during 1st year + Balanced principle amount after 1st year payment-Loan amount =10791.96-148157.98-150000=$8949.94

C)

Principal payment during 1st year =Total Payment made during 1st year- Interest paid during 1st year =10791.96-8949.94=$1842.02

D)

Total Payment made during 25th year =12*899.33=$10791.96

Balanced principle amount after 25th year payment =899.33*(1-(1+0.5%)^-60)/0.5%=$46,518.13

Balanced principle amount after 24th year payment =899.33*(1-(1+0.5%)^-72)/0.5%=$54,264.88

Interest paid during 1st year =Total Payment made during 25th year + Balanced principle amount after 25th year payment-Balanced principle amount after 24th year payment =10791.96+46518.13-54264.88=$3045.21

E)

Principal payment during 25th year =Total Payment made during 25th year- Interest paid during 25th year =10791.96-3045.21=$7746.75