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 8% 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

The break even for Emily using Option 2 presuming she is not financing the points is 7.8

Explanation:

Solution

In this case, in other to determine this problem, we need to find the monthly payments for both options

For option 1 (EMI)

Where

P = 320,000,

r =0.08/12 = 0.00667

n = 360

Now,

EMI = P *r * (1 + r)^n/  (1 + r)^n -1

So,

EMI =320,000 * 0.00667 * (1 + 0.00667)^360/ (1 + 0.00667)^360

EMI = 23329.56/9.93573

=2348.05

For Option 2

P = 320,000,

n = 360

r = 4%/12 = 0.003333

Thus,

EMI =320,000 * 0.003333 * (1 + 0.003333)^360/ (1 + 0.003333)^360

EMI = 3534.398/2.313498

=1527.73

Note:

When Emily is paying  2 discount point in the second option, she is paying the following:

2% * 320000 = 6400

Also she is saving the following:

2.348.05 - 1527.73

=820.32 on payment (monthly) because of the reduction of EMI in the second option

Thus,

The break even time is =payments  due to points/ monthly savings

=6400/820.32

=7.8

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