Example $7-4$

You plan to purchase a house for $$150,000$ using a $30-$year mortgage obtained from your local bank. You will make a down payment of $20$ percent of the purchase price. Thus, the mortgage loan amount will be $$120,000.$ Your bank offers you the following two options for payment:

Option $1$: Mortgage rate of $8$ and zero points. $($Example $7-1)$

Option $2$: Mortgage rate of $7\mathrm{.}75$ percent and $2$ points

What if you plan to pay out the mortgage within $10-$years, which option is now better?

The principle remaining for option $1$ would be $$105,269\mathrm{.}26$

The principle remaining for option $2$ would be $$104,720\mathrm{.}52$

At what maturity would you be indifference between the two options?