Question

Emily is considering purchasing a new home for $400,000. She intends to put 20% down and finance $320,000, but is unsure which financing option to select. Emily is considering the following options: o Option 1: Fixed rate mortgage over 30 years at 6% interest, zero points, or o Option 2: Fixed rate mortgage over 30 years at 4% interest, plus two discount points. How long would her financial planner recommend that she live in the house to break even using Option 2 presuming she is not financing the points?

24.6

16.4

15.9

8.2

Answer 1

First step is to calculate the monthly payments if Emily were to choose the first option i.e. without paying any discount points. The monthly payment can be calculated using the present value of annuity formula which is:

Where

• PV is the loan amount
• C is the monthly payment
• r is the interest rate
• n is the time period

Please note that since the mortgage will involve monthly payments, both interest rate and period are going to be adjusted accordingly. r is going to be 0.5% (6/12) and period 360 months.

or C = $1,918.56

Now, when she chooses the second option, she has to pay 2% of the loan amount upfront. This acts as a payment so that the lender agrees to charge a lower interest rate of 4% rather than 6%. This amount comes out to be:

= 2% of 320000 = $6,400

In return for this payment she gets to pay a lower monthly installment at a rate of 4%. The lower monthly installment comes out to:

or C = $1,527.73

The difference between the two monthly payments is $390.83 (1,918.56 - 1,527.73). This is the monthly benefit she gets in exchange for an initial payment of $6,400. The no. of months before she breaks even can be calculated by dividing the initial payment by monthly benefit. So,

So, it will take her 16.4 months to break even.