# You plan to purchase a house for $175,000 using a 15-year mortgage obtained from your local bank....

## Question:

You plan to purchase a house for $175,000 using a 15-year mortgage obtained from your local bank. You will make a down payment of 25 percent of the purchase price and monthly payments. You will not pay off the mortgage early. a. Your bank offers you the following two options for payment:

Option 1: Mortgage rate of 5 percent and zero points.

Option 2: Mortgage rate of 4.75 percent and 2 points.

Which option should you choose?

b. Your bank offers you the following two options for payments:

Option 1: Mortgage rate of 4.85 percent and 2 points.

Option 2: Mortgage rate of 4.68 percent and 3 points. Which option should you choose?

## Factors Influencing Mortgage Decisions:

There are a number of factors that can influence mortgagors when they are securing a mortgage. Some mortgagors will prioritize a 20% down payment in order to avoid default insurance and secure a lower monthly payment. For other mortgagors, saving enough money to put 20% down on a house would take years, and if they want to purchase a house sooner rather than later, they will chose to pay for default insurance and a higher monthly payment in order to purchase a home.

A desire for a smaller monthly payment could lead a home buyer to pursue the lowest possible interest rate, the maximum number of points available to buy down a mortgage, or the longest term a lender will grant them.

A home buyer who wishes to pay off his mortgage as quickly as possible will look for a shorter term with higher monthly payments and no prepayment penalties.

Home buyers are unique and their buying decisions will be influenced by a number of factors. It is important for a home buyer to understand his priorities before entering into a mortgage.

## Answer and Explanation:

We can calculate a mortgage payment amount using the following formula:

{eq}M = P ((r(1+r)^n) / ((1+r)^n - 1)) {/eq}

Where:

M | = Mortgage payment amount |

P | = Principal amount |

r | = Interest rate (expressed as a monthly rate) |

n | = Total number of payments |

a).

Option 1: 5% interest and zero points.

We must first determine our principal amount (P), our monthly interest rate (r), and our total number of payments (n).

The principal amount is the total amount of the loan. Considering the borrower will be making a 25% down payment on a home worth $175,000, we are able to determine the loan amount.

P = 175,000(1-0.25)

= 131,250

= $131,250.00

To determine our monthly interest rate, we can simply divide the annual interest rate by 12.

r = 0.05/12

= 0.0041666667

To determine our total number of payments, we multiply the number of years the loan will be in place by the number of payments that will be made each year.

n = 15 x 12

= 180

We can now enter this data into our payment formula.

M = 131,250.00 ((0.0041666667(1+0.0041666667)^180) / ((1+0.0041666667)^180 - 1))

= 1037.9166

= $1,037.92

If you accept this loan, the mortgage payment will be $1,037.92.

Option 2: 4.75% and 2 points.

2 point means that you will pay 2% of the loan value upfront to secure a lower interest rate.

This means you would pay $131,250(0.02) = $2,625 at closing.

All of our data stays the same except for the interest rate.

r = 0.0475 / 12

= 0.00395833

M = 131,250 ((0.00395833(1+0.00395833)^180) / ((1+0.00395833)^180 - 1))

= 1020.9043

= $1,020.90

If you accept this loan, the mortgage payment will be $1,020.90.

In order to determine which loan to choose, it is necessary to see whether the amount paid for the 2 points is greater than or less than the amount of interest you save over the course of the loan.

The difference in the monthly payment is:

$1,037.92 - $1,020.90 = $17.02.

The mortgage discount point costs 2% of the principal amount. This means they cost $2,625.00.

The break even point (the payment at which the interest rate savings equals the cost of the point) is:

$2,625.00 / $17.02 = 155 (rounded up to the next full payment).

This means that over the course of 180 payment (12 payments per year over 15 years) the savings from the lower interest rate will surpass the cost of purchasing the point at the 155 payment.

Because the break even point falls within the term of the loan, I would choose Option 2. Considerations that may influence this decision beyond the cost savings include whether I have an extra $2625.00 after paying all of my other home buying expenses and whether we are taking the time value of money into account.

Total cost savings from the lower interest rate are:

$17.02 x 180 = $3,063.00.

After paying $2,625.00 to buy down the rate, total amount saved would be $438.60.

b).

Option 1: 4.85% interest and 2 points.

2 point means that you will pay 2% of the loan value upfront to secure a lower interest rate.

This means you would pay $131,250(0.02) = $2,625 at closing.

The only factor that changes from our previous work is the interest rate.

To determine our monthly interest rate, we can simply divide the annual interest rate by 12.

r = 0.0485/12

= 0.004041667

We can now enter this data into our payment formula.

M = 131,250.00 ((0.004041667(1+0.004041667)^180) / ((1+0.004041667)^180 - 1))

= 1027.6899

= $1,027.69

If you accept this loan, the mortgage payment will be $1,027.69.

Option 2: 4.68% and 3 points.

3 point means that you will pay 3% of the loan value upfront to secure a lower interest rate.

This means you would pay $131,250(0.03) = $3,937.50 at closing.

All of our data stays the same except for the interest rate.

r = 0.0468 / 12

= 0.0039

M = 131,250 ((0.0039(1+0.0039)^180) / ((1+0.0039)^180 - 1))

= 1016.1698

= $1,016.17

If you accept this loan, the mortgage payment will be $1,016.17

In order to determine which loan to choose, it is necessary to see whether the amount paid for the extra 1 point in Option 2 is greater than or less than the amount of interest you save over the course of the loan.

The difference in the monthly payment is:

$1,027.69 - $1,016.17 = $11.52.

Since both mortgages pay for mortgage points, the expense differential we are considering is the difference between purchasing 3 points and 2 points. $3,937.50 - $2,625.00 = $1,312.50.

The break even point (the payment at which the interest rate savings equals the cost of the point) is:

$1,312.50 / $11.52 = 114 (rounded up to the next full payment).

This means that over the course of 180 payment (12 payments per year over 15 years) the savings from the lower interest rate will surpass the cost of purchasing the additional point at the 114 payment.

Because the break even point falls within the term of the loan, I would choose Option 2. Considerations that may influence this decision beyond the cost savings include whether I have an extra $1,312.50 after paying all of my other home buying expenses and whether we are taking the time value of money into account.

#### Learn more about this topic:

from Finance 102: Personal Finance

Chapter 7 / Lesson 4