Question

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 1

Answer:

The price of the house = $ 100000

The down payment is 20 % of 100000 means $0.20\times100000=20000$ dollars

So, loan amount will be = $100000-20000=80000$ dollars

Case A:

30-year mortgage at a rate of 7 %

p = 80000

r = $7/12/100=0.005833$

n = $30\times12=360$

EMI formula is :

$\frac{p\times r\times(1+r)^n}{(1+r)^n-1}$

Putting the values in formula we get;

$\frac{80000\times0.005833\times(1+0.005833)^360}{(1+0.005833)^360-1}$

= $\frac{80000\times0.005833\times(1.005833)^360}{(1.005833)^360-1}$

Monthly payment = $532.22

So, total amount paid in 30 years will be = $532.22\times360=191599.20$

Interest paid will be = $191599.20-100000=91599.20$ dollars

Case B:

15-year mortgage at a rate of 7 %.

Here everything will be same as above. Only n will change.

n = $15\times12=180$

Putting the values in formula we get;

$\frac{80000\times0.005833\times(1+0.005833)^180}{(1+0.005833)^180-1}$

= $\frac{80000\times0.005833\times(1.005833)^180}{(1.005833)^180-1}$

Monthly payment = $719.04

Total amount paid in 15 years will be = $719.04\times180=129427.20$

Interest paid will be = $129427.20-100000=29427.20$ dollars