You plan to purchase a house for $$600,000$ using a $30-$year mortgage. You

will make a down payment of $20$ percent of the purchase price. The loan amount is your bank

offers the following:

$$ Option $1$: Mortgage rate of $9$ percent $($monthly payments$)$

$$ Option $2$: Mortgage rate of $7$ percent and pay for $2$ points $($monthly payments$)$

a$.$ Loan amount $(2$pts$)$

b$.$ Amount spent on buying points $(2$pts$)$

c$.$ Which is the better option? $(6$pts$)$ hint: calculate the monthly payment of each option and

compare the cost of buying points to the benefits of buying points.

$7$

d$.$ Suppose you plan to pay off the mortgage in $5$ years. The principal balance of the two after

$15$ years are as follows $(5$pts$)$:

Option $1($no points$)$: $460,224\mathrm{.}83$

Option $2(2$points$)$: $451,831\mathrm{.}35$

Which is the better option? Calculate total saving from choosing option $2$ and compare it

with the cost of buying points