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: $7\mathrm{.}5\%$

Points: $0$

Mortgage B

Interest rate: $7\mathrm{.}0\%$

Points: $2$

Further instructions:

Round all answers to two decimal places.

Pay attention to negative signs.

Do not include dollar signs $($$$).$

Multiple Attempts This test allows multiple attempts.

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QUESTION $1$

You should choose the mortgage with the

Lowest total cash flows

Lowest monthly payment

Highest present value

Lowest closing costs

$10$ points

QUESTION $2$

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

$10$ points

QUESTION $3$

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

$10$ points

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.

$10$ points

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.

$10$ points

QUESTION $6$

Using a discount rate of $4\mathrm{.}6\%,$ what is the present value of the cash flows associated with Mortgage A$,$ if paid off after four years?

$10$ points

QUESTION $7$

Using a discount rate of $4\mathrm{.}6\%,$ what is the present value of the cash flows associated with Mortgage B$,$ if paid off after four years?

$10$ points

QUESTION $8$

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

Mortgage A

Mortgage B

They are the same

There is no way to tell

$10$ points

QUESTION $9$

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

Using a discount rate of $4\mathrm{.}6\backslash \%,$ what is the present value of the cash flows associated with Mortgage A$,$ if paid off after one year?

$10$ points

QUESTION $10$

Using a discount rate of $4\mathrm{.}6\backslash \%,$ what is the present value of the cash flows associated with Mortgage B$,$ if paid off after one year?

$10$ points

QUESTION $11$

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

Mortgage A

Mortgage B

They are the same

There is no way to tell