Chapter 7, Problem 12P

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 25% of the buying price, or a down payment of $43,750$\left(0.25\times 175,000\right)$ at closing and borrow $131,250 through the mortgage.

In case if the option 2 is selected and make payment of $2,625 $\left(\$131,250\times 0.02\right)$ in points and gets $128,625$\left(\$131,250-\$2,625\right)$ at closing, although the mortgage principal is $131,250. To ascertain the best option, initially the monthly payments for both options should be ascertained as follows:

• Option 1:

$\begin{array}{c}\text{\$131,250}=\text{PMT}\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0500}{12}\right)}^{15\left(12\right)}}\right)\right]}{\left(\frac{0.0500}{12}\right)}\right\}\\ \text{Solve for PMT, we get \$1,037}\text{.92}\text{.}\end{array}$

• Option 2:

$\begin{array}{c}\text{\$131,250}=\text{PMT}\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0475}{12}\right)}^{15\left(12\right)}}\right)\right]}{\left(\frac{0.0475}{12}\right)}\right\}\\ \text{Solve for PMT, we get \$1,020}\text{.90}\text{.}\end{array}$

In exchange for $2,625 upfront, option 2 decreases the monthly payments of mortgage by $17.012. The present value of these savings (ascertained at 4.75%) over the 15 years is as follows:

$\begin{array}{c}\text{PV}=\$17.012\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0475}{12}\right)}^{15\left(12\right)}}\right)\right]}{\left(\frac{0.0475}{12}\right)}\right\}\\ \text{=\$2,187}\text{.14}\end{array}$

Option 1 is best choice because the present value of monthly savings, $2,187.14, is less than the points paid up front, $2,625.

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 $2,625 $\left(\$131,250\times 0.02\right)$ in points and gets $128,625$\left(\$131,250-\$2,625\right)$ at closing, although the mortgage principal is $131,250. If the option 2 is selected and make payment of $3,937.5 $\left(\$131,250\times 0.03\right)$ in points and gets $127,312.5$\left(\$131,250-\$3,937.5\right)$ at closing. The difference in savings on the point is $1,312.5. To identify the best option the monthly payments should be computed for both options as follows:

• Option 1:

$\begin{array}{c}\text{\$131,250}=\text{PMT}\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0485}{12}\right)}^{15\left(12\right)}}\right)\right]}{\left(\frac{0.0485}{12}\right)}\right\}\\ \text{Solve for PMT, we get \$1,027}\text{.69}\text{.}\end{array}$

• Option 2:

$\begin{array}{c}\text{\$131,250}=\text{PMT}\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0468}{12}\right)}^{15\left(12\right)}}\right)\right]}{\left(\frac{0.0468}{12}\right)}\right\}\\ \text{Solve for PMT, we get \$1,016}\text{.17}\text{.}\end{array}$

In exchange for $1,312.50 upfront, option 2 decreases the monthly payments of mortgage by $11.52. The present value of these savings (ascertained at 4.68%) over the 15 years is as follows:

$\begin{array}{c}\text{PV}=\$11.52\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.0468}{12}\right)}^{15\left(12\right)}}\right)\right]}{\left(\frac{0.0468}{12}\right)}\right\}\\ \text{=\$1,487}\text{.94}\end{array}$

Option 2 is best choice because the present value of monthly savings, $1,487.94, is greater than the points paid up front, $1,312.50.