You decide to buy a house in Amherst valued at $$250,000$ and need to borrow the entire

amount to finance your house. After shopping around for a mortgage loan, you find that

the following two deals from the Financial One Company are very attractive:

$(1)$ A $15-$year fixed$-$rate mortgage with no points and an APR of $5\%,$ compounded

monthly.

$(2)$ A $15-$year fixed rate mortgage with two points and an APR of $4\mathrm{.}5\%,$ compounded

monthly. A point simply represents $1\%$ of the loan amount, and it is the front charge by

lenders to reduce the loan interest rate. The money you pay for points is tax deductible.

However, the Financial One Company does not allow you to build the point money into

the mortgage, so you need to pay the point separately. For simplicity, let$$s assume that

you have this amount of money in your bank account.

The closing costs $($not including the points$)$ for the two loans are identical.

According to the law, the interest $($points are pre$-$paid interests$)$ on your mortgage

payments are tax deductible. In fact, at the end of each year, your lender will simply add

up your $12-$month interest payments $($without considering the time value of money$)$ and

forward the mortgage statement to you and the IRS for tax filing purposes. Then you file

your tax form according to your income tax rate of $28\%.$ Assume that you pay your

mortgage payments at the end of each month, and you pay taxes at the end of each year.

A$.$ Suppose that you intend to live in the house for $15$ years. After considering all the

factors like tax savings, points, monthly payments, etc., which loan will you choose?

Discuss in detail.

B$.$ If you plan to live in the house for only five years, how does this affect your choice?

Discuss in detail.

C$.$ Suppose that you chose the $5\%$ loan to finance your house. Five years have passed

since you purchased the house. You have paid $60$ monthly payments with no additional

payments toward the principal. The current APR for the $10-$year fixed$-$rate mortgage is

$4\mathrm{.}25\%$ with no point. The Financial Two Company offers you a chance to refinance your

original loan with the current $4\mathrm{.}25\%$ loan. They will charge you a $$2,500$ refinancing fee.

This fee is not tax deductible. After considering all the factors, should you take Financial

Two$$s offer to refinance your loan outstanding? Why or why not?

Make assumptions wherever applicable and explain your answers in detail.