Answer
The mortgage option that has greater total cost is \[\text{Mortgage A}\]and by\[\$53,910\].
For option A:
First of all, compute the value of the one point by multiplying the amount of mortgage with the one point, use the equation as shown below:
\[\begin{align}
& \text{One point Amount}=\text{Mortgage Amount}\times 0.011 \\
& =\$250,000\times0.01\\&=\$\text{2,500}\end{align}\]
The one point amount in option A that needs to be paid at the closing is $2,500.
Now, it is required to compute the monthly payment value for the $250,000 mortgage at 7.25% for 30 years. Compute the monthly payment by substituting the values in the loan payment formula as shown below:
\[\begin{align}
& PMT=\frac{P\left( \frac{r}{n} \right)}{\left( 1-{{\left( 1+\frac{r}{n} \right)}^{-nt}} \right)} \\
& =\frac{\$250,000\times\left(\frac{0.0725}{12}\right)}{1-{{\left(1+\frac{0.0725}{12}\right)}^{-12\times30}}}\\&=\frac{\$250,000\times\left(0.00604\right)}{1-{{\left(1+0.00604\right)}^{-360}}}\\&=\$1,706\end{align}\]
In order to calculate the interest amount that will be paid in 30 years, subtract the amount of total monthly payments with the amount of mortgage, use below equation:
Work Step by Step
