Question

Use the following to answer questions 1-4.

You currently live (rent free) in your parents' basement but it's a bit awkward when you bring dates home. Your friends are looking for a new roommate and have asked if you're interested in moving in. Your share of the rent (which includes all utilities) will be $1,000 per month, due at the beginning of the month, and you will be signing a three-year lease.

You parents think you should save your money so you can buy a house when you graduate in three years. If you stay living in your parents' basement, and deposit the money you save by not having to pay rent into a savings account at the beginning of each month, your parents have offered to give you a gift equal to the amount you have saved towards a down payment on your first home. Assume the bank is offering a 5% annual interest rate, compounding monthly, on new savings accounts.

1. Your monthly rent payment in this example would be considered _________________.

A) an ordinary annuity

B) an annuity due

C) amortization

D) a perpetuity

2. If you take your parents up on their offer, how much will have (in total) for a down payment on a home when you graduate? Round your final answer to the nearest whole dollar. * Hint: remember your parents have offered to match what you save on your own.

A) $36,000

B) $38,915

C) $77,507

D) $77,830

3. Suppose you took your parents up on their offer and are now getting ready to graduate. You have decided that you can afford a house payment of $1,200 per month. You received quotes from several lenders and determined that the most likely annual interest rate you will be offered is 4.75% for a 30 year, fixed rate mortgage. What is the maximum you can pay for a house? Round to the nearest whole dollar. Hints: (1) Mortgage payments are in arrears (meaning they are paid at the END of the time period). Be sure your calculator is in the correct mode before solving. (2) After you solve for the maximum loan amount, don't forget to add on your down payment to determine the sales price!

A) $230,041

B) $269,866

C) $307,871

D) $308,781

4. Would you be required to pay PMI with this loan?

A) Yes

B) No

Use the following to answer questions 5-7.

You have selected the lender you will be using and completed the application process. You are excited to find out that your credit score was better than you originally thought when estimating how much you could spend on a house. You are being offered a lower interest rate than you were originally quoted on two different loan options. Both are 30 year, fixed rate mortgages with payments of $1,000 per month and origination fees equal to 2% of the loan amount. * hints (1) Assume these loans have zero PMI (2) you have additional money set aside to cover closing costs so you are using the full amount from #2 as a down payment.

   · Loan A has an APR of 4% with no points.

   · Loan B has an APR of 3.90% with 1.5 points.

5. What is your Effective borrowing cost if you select Loan A? Enter your answer as a whole number with 3 decimal points (no percent sign).

6. What is your Effective borrowing cost if you select Loan B? Enter your answer as a whole number with 3 decimal points (no percent sign).

7. Assuming you intend to stay in the house for 30 years, which loan should you choose? *hint: Answer using the calculations you did in questions 5 and 6 rather than relying on the “rule of thumb” about EBC and loan choices presented in the text and on the slides.

A) Loan A

B) Loan B

Answer the remaining questions assuming you opted for Loan A.

8. You decide to rent out a room in your new home to your best friend for $500 per month. If you add the extra money to your monthly house payment, how many years will it take you to pay off your mortgage?

A) 15.69 years

B) 17.72 years

C) 30 years

D) 158 years

Please answer all parts of questions with since they connect! Please and thank you and use TVM formulas

Answer 1

1]

B) an annuity due. This is because each payment is equal and made at the beginning of the period.

A is incorrect. An ordinary annuity is made at the end of each period.

C is incorrect - An amortization refers to a loan where principal is paid off over time.

D is incorrect - In a perpetuity, cash flows are made forever.

2]

D) $77,830

This is calculated as below :

Change the calculator into "Begin" mode, as each payment is made at the beginning of the month.

I/Y = 5/12 (monthly rate = annual rate / 12 = 5%/12)

N = 36 (3 years with 12 monthly payments each year = 3 * 12 = 36)

PMT = -2000 (monthly payment. This is entered with a negative sign as it is a payment)

PV = 0 (beginning amount in savings is zero)

CPT --> FV

FV is calculated to be $77,830.

3]

Maximum loan amount is calculated as below :

Change the calculator into "End" mode, as each payment is made at the end of the month.

I/Y = 4.75/12 (monthly rate = annual rate / 12 = 4.75%/12)

N = 360 (30 years with 12 monthly payments each year = 30 * 12 = 360)

PMT = -1200 (monthly payment. This is entered with a negative sign as it is a payment)

CPT --> PV

PV is calculated to be $230,041. This is the maximum loan amount.

Maximum cost of house = maximum loan amount + down payment

Maximum cost of house = $230,041 + $77,830 = $307,871

d]

PMI is required if the down payment is less than 20% of the home's price.

In this case, down payment % =  $77,830 / $307,871 = 25%

Therefore, PMI is not required.