Mr. Smith is purchasing a $ 100000 house. The down payment is 20 % of the price of the house. He is given the choice of two mortgages:a) a 30-year mortgage at a rate of 7 %.Find: (i) the monthly payment: $ (ii) the total amount of interest paid: $b) a 15-year mortgage at a rate of 7 %.Find: (i) The monthly payment:$ (ii) the total amount of interest paid: $

Answer:The price of the house = $ 100000 The down payment is 20 % of 100000 means [tex]0.20\times100000=20000[/tex] dollarsSo, loan amount will be = [tex]100000-20000=80000[/tex] dollarsCase A:30-year mortgage at a rate of 7 %p = 80000r = [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 = $532.22So, 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] dollarsCase 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 = $719.04Total 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