Question

I’m trying to solve this problem and need assistance with it

Answer 1

Given:

• Cost of house = $450,000

,

• Down payement = 20% ==> 0.20

,

• Time for mortgage A = 30 years

,

• Rate of mortgage A = 2.65%

,

• Time for mortgage B = 15 years

,

• Rate of mortgage B = 2.02%

Let's solve for the following:

• (a). Which mortgage will give the lowest payment and what will the payemnt be?

Since you have made a down payement of 20%, the amount left to be paid will be:

`\begin{gathered} A=450000(1-0.20) \\ A=450000(0.80) \\ A=360000 \end{gathered}`

The amount left to be paid is $360,000

Apply the monthly payment formula:

`A=P((r)/(12)(1+(r)/(12))^n)/((1+(r)/(12))^n-1)`

For mortgage A:

P = 360000

r = 2.65 ==> 0.0265

n is the number of months = 30 years x 12 = 360 months

Substitute values in the formula and solve for A:

`\begin{gathered} A=360000*\frac{(0.0265)/(12)(1+(0.0265)/(12))^(360)^{}}{(1+(0.0265)/(12))^(360)-1} \\ \\ A=360000*(0.0048859)/(1.21250084) \\ \\ A=1450.67 \end{gathered}`

Therefore, the monthly payments for mortgage A is $1,450.67

For mortgage B:

P = 360000

r = 2.02% ==> 0.0202

n = 15 x 12 = 180

Thus, we have:

`\begin{gathered} A=360000*((0.0202)/(12)(1+(0.0202)/(12))^(180))/((1+(0.0202)/(12))^(180)-1) \\ \\ \\ A=2319.95 \end{gathered}`

The monthly payement for mortgage B is $2319.95

Mortgage A(30 year) will give the lowest monthly payement of $1450.67

Difference = $2319.95 - $1450.67 = $869.28

The 30 year Mortgage will be $869.28 lower than the 15 year mortgage.

• (b). If you take the full term mortgage let's determine the mortgage which will result in you apying the most interest.

Apply the formula:

Interest = (A x n) - P

Mortgage A:

`\text{Interest}=(1450.67*360)-360000=162241.20`

The total interest for the 30 year mortgage is $162241.20

Mortgage B:

`\text{Interest}=(2319.95*180)-360000=57591`

The total interest for the 15-year mortgage is $57591

Therefore, mortage A will result in you paying the most interest.

Difference = $162241.20 - $57591 = $104650.20

The interest for mortgage B will be $104650.20 lesser than the total interst of A.

ANSWER:

(a). Mortgage A(30 year) will give the lowest monthly payement of $1450.67

The monthly payment 30 year Mortgage will be $869.28 lower than the 15 year mortgage.

(b). Mortage A will result in you paying the most interest of $162241.20

The total interest for mortgage B will be $104650.20 lesser than the total interest of A.