Question

When obtaining a mortgage, one choice you make is whether to pay points in exchange for a lower interest rate. This homework asks you to work through the math to decide whether to do so.

Scenario Details:

Amount of mortgage: $500,000
Other closing costs: $6,500
Length of mortgage: 30 years
Mortgage interest compounds monthly, and payments are monthly
Expected duration of residence: 4 years
Mortgage Options:

Mortgage A
Interest rate: 7.5%
Points: 0
Mortgage B
Interest rate: 7.0%
Points: 2

Further instructions:
Round all answers to two decimal places.
Pay attention to negative signs.
Do not include dollar signs ($).

QUESTION 1

You should choose the mortgage with the

a.Lowest total cash flows
b.Lowest closing costs
c.Highest present value
d.Lowest monthly payment

QUESTION 2

What is the payment for Mortgage A (rounded to two decimal places)?

QUESTION 3

What is the payment for Mortgage B (rounded to two decimal places)?

QUESTION 4

When you payoff your mortgage in four years, how much will that lump sum payment be for Mortgage A? Be sure to use the rounded mortgage payment in this calculation.

QUESTION 5

When you pay off your mortgage in four years, how much will that lump sum payment be for Mortgage B? Be sure to use the rounded mortgage payment in this calculation.

QUESTION 6

Using a discount rate of 4.6%, what is the present value of the cash flows associated with Mortgage A, if paid off after four years?

QUESTION 7

Using a discount rate of 4.6%, what is the present value of the cash flows associated with Mortgage B, if paid off after four years?

QUESTION 8

Which mortgage is the better choice if you pay the mortgage off after four years?

a.Mortgage A
b.Mortgage B
c.They are the same
d.There is no way to tell

QUESTION 9

The remaining questions explore how the answers change if you repay the mortgage after just one year.

Using a discount rate of 4.6\%, what is the present value of the cash flows associated with Mortgage A, if paid off after one year?

QUESTION 10

Using a discount rate of 4.6\%, what is the present value of the cash flows associated with Mortgage B, if paid off after one year?

QUESTION 11

Which mortgage is the better choice if you pay the mortgage off after one year?

a.Mortgage A
b.Mortgage B
c.They are the same
d.There is no way to tell

Answer 1

In this scenario, Mortgage A has the lowest total cash flows and would be the better choice if the mortgage is paid off after four years. The monthly payment for Mortgage A is $3494.82, while the monthly payment for Mortgage B is $3321.56. The lump sum payment for Mortgage A when paid off after four years is $201,784.89, and for Mortgage B, it is $193,990.71. Using a discount rate of 4.6%, the present value of the cash flows associated with Mortgage A, if paid off after four years, is $184,171.20, while for Mortgage B, it is $174,767.48.

Step-by-step explanation:

QUESTION 1

You should choose the mortgage with the lowest total cash flows.

QUESTION 2

The payment for Mortgage A is $3494.82.

QUESTION 3

The payment for Mortgage B is $3321.56.

QUESTION 4

The lump sum payment for Mortgage A, when paid off after four years, is $201,784.89.

QUESTION 5

The lump sum payment for Mortgage B, when paid off after four years, is $193,990.71.

QUESTION 6

The present value of the cash flows associated with Mortgage A, if paid off after four years and using a discount rate of 4.6%, is $184,171.20.

QUESTION 7

The present value of the cash flows associated with Mortgage B, if paid off after four years and using a discount rate of 4.6%, is $174,767.48.

QUESTION 8

Based on the calculations, the better choice if you pay the mortgage off after four years is Mortgage A.

QUESTION 9

Using a discount rate of 4.6%, the present value of the cash flows associated with Mortgage A, if paid off after one year, is $178,594.74.

QUESTION 10

Using a discount rate of 4.6%, the present value of the cash flows associated with Mortgage B, if paid off after one year, is $168,708.60.

QUESTION 11

Based on the calculations, the better choice if you pay the mortgage off after one year is Mortgage A.