Chapter 7, Problem 11P

a)

Summary Introduction

To determine: The best option from the given two options.

Explanation of Solution

For both the mortgage the down payment will be 20% of the buying price, or a down payment of $39,000$\left(0.20\times 195,000\right)$ at closing and borrow $156,000 through the mortgage.

In case if the option 2 is selected and make payment of $2,340 $\left(\$156,000\times 0.015\right)$ in points and gets $153,660$\left(\$156,000-\$2,340\right)$ at closing, although the mortgage principal is $156,000. To ascertain the best option, initially the monthly payments for both options should be ascertained as follows:

• Option 1:

$\begin{array}{c}\text{\$156,000}=\text{PMT}\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0550}{12}\right)}^{30\left(12\right)}}\right)\right]}{\left(\frac{0.0550}{12}\right)}\right\}\\ \text{Solve for PMT, we get \$885}\text{.75}\text{.}\end{array}$

• Option 2:

$\begin{array}{c}\text{\$156,000}=\text{PMT}\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0535}{12}\right)}^{30\left(12\right)}}\right)\right]}{\left(\frac{0.0535}{12}\right)}\right\}\\ \text{Solve for PMT, we get \$871}\text{.13}\text{.}\end{array}$

In exchange for $2,340 upfront, option 2 decreases the monthly payments of mortgage by $14.625. The present value of these savings (ascertained at 5.35%) over the 30 years is as follows:

$\begin{array}{c}\text{PV}=\$14.625\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0535}{12}\right)}^{30\left(12\right)}}\right)\right]}{\left(\frac{0.0535}{12}\right)}\right\}\\ \text{=\$2,619}\text{.11}\end{array}$

Option 2 is best choice because the present value of monthly savings, $2,619.11, is greater than the points paid up front, $2,340.

b)

Summary Introduction

To determine: The best option from the given two options.

Explanation of Solution

In case if the option 1 is selected and make payment of $1,560 $\left(\$156,000\times 0.01\right)$ in points and gets $154,440$\left(\$156,000-\$1,560\right)$ at closing, although the mortgage principal is $156,000. If the option 2 is selected and make payment of $3,120 $\left(\$156,000\times 0.02\right)$ in points and gets $152,880$\left(\$156,000-\$3,120\right)$ at closing. The difference in savings on the point is $1,560. To identify the best option the monthly payments should be computed for both options as follows:

• Option 1:

$\begin{array}{c}\text{\$156,000}=\text{PMT}\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0535}{12}\right)}^{30\left(12\right)}}\right)\right]}{\left(\frac{0.0535}{12}\right)}\right\}\\ \text{Solve for PMT, we get \$871}\text{.125}\text{.}\end{array}$

• Option 2:

$\begin{array}{c}\text{\$156,000}=\text{PMT}\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0525}{12}\right)}^{30\left(12\right)}}\right)\right]}{\left(\frac{0.0525}{12}\right)}\right\}\\ \text{Solve for PMT, we get \$861}\text{.438}\text{.}\end{array}$

In exchange for $1,560 upfront, option 2 decreases the monthly payments of mortgage by $9.687. The present value of these savings (ascertained at 5.25%) over the 30 years is as follows:

$\begin{array}{c}\text{PV}=\$9.687\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0525}{12}\right)}^{30\left(12\right)}}\right)\right]}{\left(\frac{0.0525}{12}\right)}\right\}\\ \text{=\$1,754}\text{.24}\end{array}$

Option 2 is best choice because the present value of monthly savings, $1,754.24, is greater than the points paid up front, $1,560.