Chapter 7, Problem 10P

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 $115,000 buying price of a new home, or a down payment of 23,000$\left(0.20\times 115,000\right)$ at closing and borrow $92,000 through the mortgage.

In case if the option 2 is selected and make payment of $1,840 $\left(\$92,000\times 0.02\right)$ in points and gets $90,160$\left(\$92,000-\$1,840\right)$ at closing, although the mortgage principal is $92,000. To ascertain the best option, initially the monthly payments for both options should be ascertained as follows:

• Option 1:

$\begin{array}{c}\text{\$92,000}=\text{PMT}\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0900}{12}\right)}^{30\left(12\right)}}\right)\right]}{\left(\frac{0.0900}{12}\right)}\right\}\\ \text{Solve for PMT, we get \$740}\text{.25}\text{.}\end{array}$

• Option 2:

$\begin{array}{c}\text{\$92,000}=\text{PMT}\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0885}{12}\right)}^{30\left(12\right)}}\right)\right]}{\left(\frac{0.0885}{12}\right)}\right\}\\ \text{Solve for PMT, we get \$730}\text{.35}\text{.}\end{array}$

In exchange for $1,840 upfront, option 2 decreases the monthly payments of mortgage by $9.90. The present value of these savings (ascertained at 8.85%) over the 30 years is as follows:

$\begin{array}{c}\text{PV}=\$9.90\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0885}{12}\right)}^{30\left(12\right)}}\right)\right]}{\left(\frac{0.0885}{12}\right)}\right\}\\ \text{=\$1,248}\text{.06}\text{.}\end{array}$

Option 1 is best choice because the present value of monthly savings, $1,248.06, is less than the points paid up front, $1,840.

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 $920 $\left(\$92,000\times 0.01\right)$ in points and gets $91,080$\left(\$92,000-\$920\right)$ at closing, although the mortgage principal is $92,000. If the option 2 is selected and make payment of $2,300 $\left(\$92,000\times 0.025\right)$ in points and gets $89,700$\left(\$92,000-\$2,300\right)$ at closing. The difference in savings on the point is $1,380. To identify the best option the monthly payments should be computed for both options as follows:

• Option 1:

$\begin{array}{c}\text{\$92,000}=\text{PMT}\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.1025}{12}\right)}^{30\left(12\right)}}\right)\right]}{\left(\frac{0.1025}{12}\right)}\right\}\\ \text{Solve for PMT, we get \$824}\text{.413}\text{.}\end{array}$

• Option 2:

$\begin{array}{c}\text{\$92,000}=\text{PMT}\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.1000}{12}\right)}^{30\left(12\right)}}\right)\right]}{\left(\frac{0.1000}{12}\right)}\right\}\\ \text{Solve for PMT, we get \$807}\text{.366}\text{.}\end{array}$

In exchange for $1,380 upfront, option 2 decreases the monthly payments of mortgage by $17.047. The present value of these savings (ascertained at 10%) over the 30 years is as follows:

$\begin{array}{c}\text{PV}=\$17.047\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.1000}{12}\right)}^{30\left(12\right)}}\right)\right]}{\left(\frac{0.1000}{12}\right)}\right\}\\ \text{=\$1,942}\text{.52}\end{array}$

Option 2 is best choice because the present value of monthly savings, $1,942.52, is less than the points paid up front, $1,380.