Case Information:

Mary Jones is in the market for a new home. She will need a $$375,000$ mortgage in order to purchase her $$dream house.$$ Mary is meeting with a loan officer at her bank to discuss some loan options. Information about these options is given below and should help you answer the $6$ questions for this case. The seller of her potential new home has agreed to pay for the closing costs in order to entice buyers.

Mortgage Option #$1$: $30-$year fixed rate mortgage:

A $30-$year home mortgage is the most popular option chosen by potential homeowners. This loan would be repaid in equal monthly installments. The monthly installment payments are made up of principal payments $($which reduce the principal of the loan$)$ and interest payments $($paid to the bank for the use of the money$).$ Since Mary has an excellent credit rating, the bank has offered her $5\mathrm{.}25\%$ annual loan rate.

Mortgage Option #$2$: $20-$year fixed rate mortgage:

The bank also has a $20-$year fixed rate mortgage. This loan would also be repaid in equal monthly installments and the bank is willing to offer Mary the same $5\mathrm{.}25\%$ annual loan rate.

Mortgage Option #$3$: SMART loan:

A smart loan works as follows: every two weeks, Mary will make a mortgage payment that is $(1)/(2)$ of the amount that she would pay for her monthly $30-$year mortgage. The APR for the SMART loan is the same as that of the $30-$year fixed rate mortgage. This option would save interest as compared to the $30-$year fixed rate mortgage option.

Mortgage Option #$4$: Bullet Loan:

The loan officer also mentions a bullet loan, which will provide a greater interest savings. For the first $60$ months, Mary would pay the bank the same monthly payment as she would for the $30-$year fixed rate mortgage. However, the $$bullet$$ payment is due immediately after the $60$th payment is paid. The $$bullet$$ payment occurs as Mary must pay the remaining principal on her loan at that time. The remaining principal can be shown as the ending balance in an amortization table after $60$ payments are made. Alternatively, this principal balance may be calculated as a present value of this loan considering $25$ years are left on the loan $($note that this should be shown as months in the PV calculation$).$

Mortgage Option #$5$: Interest Only Loan:

There is a final mortgage option that the loan officer presents to Mary. An interest$-$only loan is typically not offered for consumer loans, but the bank has a trial that it is offering currently. For the interest only loan, Mary does not have to make any principal payments on the loan until it is due $10$ years from now. In the meantime, she makes monthly interest only payments. The APR for this loan is $3\mathrm{.}9\%.$

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Case Questions$/$Information:

The responses to the case questions must be typed. For F$2$F sections, students must turn in a printed copy by the beginning of class on the day that the case is due. For fully online classes, please submit your case to Blackboard$$s $$Cases$$ tab. You may work alone or in a group of up to $4$ students. Only $1$ copy of the case is required for any groups, but please be sure that all students$$ names are included on that copy. You should use an Excel spreadsheet to show your calculations. Any text responses $($#$3$c and #$6$b$)$ can be typed in the Excel spreadsheet or printed via a word processor.

Question #$1$:

a$.$ What are the monthly payments for the $30-$year fixed rate mortgage? $(5$ points$)$

b$.$ What are the monthly payments for the $20-$year fixed rate mortgage? $(5$ points$)$

Question #$2$:

a$.$ Prepare an amortization table for the first $6$ months for the $30-$year fixed rate mortgage. $(15$ points$)$

b$.$ How much of the first payment goes toward the loan$$s principal? $(5$ points$)$

Question #$3$:

a$.$ How many periods would it take to pay off the SMART loan? $(5$ points$)$

b$.$ Convert the number of periods to show how many years it would take to pay off the SMART loan. $(5$ points$)$

c$.$ Why is this shorter than the time needed to pay off the $30-$year fixed rate mortgage? $(5$ points$)$

d$.$ How much money would Mary save in interest if she took the SMART loan as compared to the $30-$year fixed rate mortgage? Hint: take the difference of the total of all payments for the $30-$year fixed rate loan and the total of all the payments for the SMART loan. $(5$ points$)$

Question #$4$:

a$.$ How much does Mary pay for each of the $60$ monthly payments for the Bullet loan? $(5$ points$)$

b$.$ How much is the bullet? Remember that the bullet is the principal remaining on the loan after the $60$ payments are made. $(10$ points$)$

Question #$5$:

a$.$ How much does Mary pay for each of the $120$ monthly payments for the interest only loan? $(5$ points$)$

b$.$ How much does Mary owe the bank after she makes the $120$ monthly payments? While she can make additional principal payments during the term of the loan, for this calculation consider that she does not make any additional principal payments. $(10$ points$)$

Question #$6$:

a$.$ Find the E$.$A$.$R$.($effective annual rates$)$ for the $5$ types of mortgages that Mary is considering. $(10$ poi