Financial Markets and Institutions (The Mcgraw-hill / Irwin Series in Finance, Insurance and Real Estate)
Financial Markets and Institutions (The Mcgraw-hill / Irwin Series in Finance, Insurance and Real Estate)
6th Edition
ISBN: 9780077861667
Author: Anthony Saunders Professor, Marcia Millon Cornett
Publisher: McGraw-Hill Education
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Chapter 7, Problem 10P

a)

Summary Introduction

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

a)

Expert Solution
Check Mark

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(0.20×115,000) at closing and borrow $92,000 through the mortgage.

In case if the option 2 is selected and make payment of $1,840 ($92,000×0.02) in points and gets $90,160($92,000$1,840) 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:

$92,000=PMT{[1(1(1+0.090012)30(12))](0.090012)}Solve for PMT, we get $740.25.

  • Option 2:

$92,000=PMT{[1(1(1+0.088512)30(12))](0.088512)}Solve for PMT, we get $730.35.

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:

PV=$9.90{[1(1(1+0.088512)30(12))](0.088512)}=$1,248.06.

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.

b)

Expert Solution
Check Mark

Explanation of Solution

In case if the option 1 is selected and make payment of $920 ($92,000×0.01) in points and gets $91,080($92,000$920) at closing, although the mortgage principal is $92,000. If the option 2 is selected and make payment of $2,300 ($92,000×0.025) in points and gets $89,700($92,000$2,300) 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:

$92,000=PMT{[1(1(1+0.102512)30(12))](0.102512)}Solve for PMT, we get $824.413.

  • Option 2:

$92,000=PMT{[1(1(1+0.100012)30(12))](0.100012)}Solve for PMT, we get $807.366.

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:

PV=$17.047{[1(1(1+0.100012)30(12))](0.100012)}=$1,942.52

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.

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