Answer:
119 months
Step-by-step explanation:
In this question, we are asked to calculate the amount of time it would take for a break-even point on a mortgage, if there is a factoring in the cost of points.
We proceed to answer the;
Mathematically,
The Break Even Point = Amount Paid for purchasing Discount Points divided by Monthly savings in the interest payments
We lost out the important values given in the question as follows:
Amount of Mortgage - $675,250
Tenure - 30 Years
The Rate of interest without points = 7.25%
The number of points = 3 points
The rate of interest with the 3 points = 6.875%
The amount to be paid for purchasing the discount point is now calculated below;
Since 1 discount point = 1% of mortgage value;
Therefore, 3 discount points = 3% of mortgage value
The amount paid is thus = 3% of $675,250 = $20,257.5
To calculate Monthly payment without points, we use the mathematical formula;
M = P[r(1+r)^n/((1+r)^n)-1)]
Where M
Is monthly payment, r is the interest rate, n is the number of months.
According to the question M = 675,250, r = 7.25% = 7.25/100 = 0.0725 , n= 30 * 12 months = 360 months
M = 675,250[0.0725(0.0725+1)^30/(1+0.0725)^360)-1) = $4606.40
To get the monthly payment with points, we simply use the formula again but this time interest rates will be 6.875% = 0.06875 I.e r = 0.06875
Inputting the terms in the formula will yield a value of $4435.91. This means monthly payment with discount will be $4435.91
Savings in monthly payments after purchasing the discount points = $4,606.40 - $4,435.91 = $170.48
Break Even = Purchase cost of Discount Points / Monthly savings
= $20,257.5 / $170.48
= 119 Months
Hence, the number of months it will take Lisa and Lenny to break-even point on their mortgage will be 119 months
