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

Answer 1

It would take $\boxed{\bf 9\text{\bf years}}$ to broke even by buying $1$ point.

Further explanation

Given:

A Monthly mortgage payment will be $\ 958$ without buying points and monthly mortgage payment will be reducing to $\ 948.75$ buying $1$ point.

This implies that the monthly mortgage payment decreases by buying $1$ point.

Subtract $\948.75$ from $\958$.

$\boxed{958-948.75=9.25}$

From the above calculation it is concluded that after buying $1$ point the monthly mortgage payment reduces by $\ 9.25$.  

The amount by which the yearly mortgage payment decreases is calculated as follows:

$\boxed{12\times 9.25=111}$

It is given that the cost of $1$ point is $\ 1000$.

The required number of years to break even by buying $1$ point is calculated as follows:

$\fbox{\begin\\\ \begin{aligned}n&=\dfrac{1000}{111}\\&=9.009\\ &\approx9\end{aligned}\\\end{minispace}}$

Therefore, it would take $\boxed{\bf 9\text{\bf years}}$ to break even by buying $1$ point.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Ratio and proportion

Keywords: Monthly payment, buying points, ratio, proportion, real numbers, integers, rational numbers, interest, marginal cost, revenue cost, selling price, cost price, percentage .

Answer 2

The answer to the problem is c