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:
[tex]\begin{gathered} A=450000(1-0.20) \\ A=450000(0.80) \\ A=360000 \end{gathered}[/tex]The amount left to be paid is $360,000
Apply the monthly payment formula:
[tex]A=P\frac{\frac{r}{12}(1+\frac{r}{12})^n}{(1+\frac{r}{12})^n-1}[/tex]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:
[tex]\begin{gathered} A=360000\times\frac{\frac{0.0265}{12}(1+\frac{0.0265}{12})^{360}^{}}{(1+\frac{0.0265}{12})^{360}-1} \\ \\ A=360000\times\frac{0.0048859}{1.21250084} \\ \\ A=1450.67 \end{gathered}[/tex]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:
[tex]\begin{gathered} A=360000\times\frac{\frac{0.0202}{12}(1+\frac{0.0202}{12})^{180}}{(1+\frac{0.0202}{12})^{180}-1} \\ \\ \\ A=2319.95 \end{gathered}[/tex]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:
[tex]\text{Interest}=(1450.67\times360)-360000=162241.20[/tex]The total interest for the 30 year mortgage is $162241.20
Mortgage B:
[tex]\text{Interest}=(2319.95\times180)-360000=57591[/tex]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.
