Question

Without buying points, a monthly mortgage payment will be $958. Buying 1 point at closing would reduce the payment to $948. 75. If each point costs $1000. 00, rounded to the nearest year, how long would it take to break even by buying 1 point? a. 7 years b. 8 years c. 9 years d. 10 years Please select the best answer from the choices provided A B C D.

Answer 1

The time taken to break even at buying 1 point will be in 9 years.

Given,

• Monthly mortgage payment =$958
• Monthly payment will be reduced to buy 1 point =$948.75
• Cost of each point =$1,000

Computation:

1. The computation of the reduced amount in the monthly mortgage payment:

$\begin{aligned}\text{Reduced Amount}&=\text{Original Payment}-\text{Reduced Payment}\\&=\ 958-\ 948.75\\&=\ 9.25\end{aligned}$

2. The computation of yearly mortgage payment:

$\begin{aligned}\text{Yearly Mortgage Payment}&=\text{Reduced Amount}\times\text{Total Months in a Year}\\&=\ 9.25\times12\\&=\ 111\end{aligned}$

3. The computation of the number of years for the break-even by buying 1 point:

$\begin{aligned}\text{Number of Years}&=\dfrac{\text{Cost of Point}}{\text{Amount og Yearly Mortgage Payment}}\\&=\dfrac{\ 1,000}{\ 111}\\&=9.00\;\text{Years}\end{aligned}$

Therefore, to break even by buying 1 point the holder requires 9 years to reach.

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