Respuesta :
Answer:
The price of the house = $ 100000
The down payment is 20 % of 100000 means [tex]0.20\times100000=20000[/tex] dollars
So, loan amount will be = [tex]100000-20000=80000[/tex] dollars
Case A:
30-year mortgage at a rate of 7 %
p = 80000
r = [tex]7/12/100=0.005833[/tex]
n = [tex]30\times12=360[/tex]
EMI formula is :
[tex]\frac{p\times r\times(1+r)^n}{(1+r)^n-1}[/tex]
Putting the values in formula we get;
[tex]\frac{80000\times0.005833\times(1+0.005833)^360}{(1+0.005833)^360-1}[/tex]
= [tex]\frac{80000\times0.005833\times(1.005833)^360}{(1.005833)^360-1}[/tex]
Monthly payment = $532.22
So, total amount paid in 30 years will be = [tex]532.22\times360=191599.20[/tex]
Interest paid will be = [tex]191599.20-100000=91599.20[/tex] dollars
Case B:
15-year mortgage at a rate of 7 %.
Here everything will be same as above. Only n will change.
n = [tex]15\times12=180[/tex]
Putting the values in formula we get;
[tex]\frac{80000\times0.005833\times(1+0.005833)^180}{(1+0.005833)^180-1}[/tex]
= [tex]\frac{80000\times0.005833\times(1.005833)^180}{(1.005833)^180-1}[/tex]
Monthly payment = $719.04
Total amount paid in 15 years will be = [tex]719.04\times180=129427.20[/tex]
Interest paid will be = [tex]129427.20-100000=29427.20[/tex] dollars
