Laura and martin obtain a 25 year 120,000 conventional mortgage at 8.5% on a house selling for 140,000 their monthly mortgage payment including principal and interest is 966 dollars

a) Determine the total amount they will pay for their house

b) How much of the cost will be interest?

c) How much of the first payment on the mortgage is applied to the principal?

Answer:

a) [tex]X=\$289800[/tex]

b) [tex]I=\$169800[/tex]

c) [tex]Y=\$116[/tex]

Step-by-step explanation:

From the question we are told that:

Time [tex]T=25years =>300 months[/tex]

Initial Mortgage [tex]N=140,000[/tex]

Mortgage [tex]N'=120,000[/tex]

Rate [tex]r=8.5\%=>0.085[/tex]

Monthly Mortgage payment P=\%966

a)

The total amount Payable X is mathematically given as

[tex]X=Monthly\ Mortgage\ payment*Number\ of\ months[/tex]

[tex]X=966*300[/tex]

[tex]X=\$289800[/tex]

b)

Generally the equation for Interest I is mathematically given by

[tex]Interest= Total\ amount\ Payable -Mortgage N'[/tex]

[tex]I=289800-120000[/tex]

[tex]I=\$169800[/tex]

c)

Generally the equation for Interest I is mathematically given by

[tex]I=Ptr[/tex]

Where

[tex]t= Month +.1month=>1/12[/tex]

Therefore

[tex]I=120000*1/12*0.085[/tex]

[tex]I=850[/tex]

Therefore the first payment on the mortgage is applied to the principal is

[tex]Y=\$966-850[/tex]

[tex]Y=\$116[/tex]