without buying points, a monthly mortgage payment will be $1,250. buying 1 point at closing would reduce the…

without buying points, a monthly mortgage payment will be $1,250. buying 1 point at closing would reduce the payment to $1,236. to the nearest year, how long would it take to break even by buying 1 point, with a $100,000 mortgage?\n a. 5 years\n b. 6 years\n c. 7 years\n d. 8 years\n please select the best answer from the choices provided
Answer
Explanation:
Step1: Calculate monthly savings
The monthly savings by buying 1 - point is $1250 - 1236=$14$.
Step2: Calculate the cost of 1 point
One point is 1% of the mortgage amount. For a $100,000 mortgage, the cost of 1 point is $0.01\times100000 = $1000$.
Step3: Calculate the number of months to break - even
The number of months $n$ to break - even is given by the formula $n=\frac{\text{Cost of 1 point}}{\text{Monthly savings}}$. So, $n=\frac{1000}{14}\approx71.43$ months.
Step4: Convert months to years
To convert months to years, divide the number of months by 12. $n_{years}=\frac{71.43}{12}\approx6$ years.
Answer:
B. 6 years