Answer:
The break even for Emily using Option 2 presuming she is not financing the points is 7.8
Step-by-step 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