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 annuityB) 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

Answer 1

1)

b)

annuity due (since payments are made at start of month)

2)

Amount available for downpayment

=

monthly contribution*(1+r)*FVAF(rate,time)

Monthly contribution

=

1000+1000=$2000

Rate

=

0.05/12=0.004166666 per month

Time

=

3 years* 12 months=36 months

Amount available for downpayment

=

2000*(1+0.00416667)[{(1+0.04166667)36}-1]/0.00466667

=

2000*1.004166667*38.75334

=

$77,830

The answer is option (D) $77830

3)

Present value of loan

=

monthly payment*PVAF(rate,time)

rate

=

0.0475/12=0.003958 per month

time

=

30years*12 months=360months

Present value of loan

=

1200*PVAF(0.003958,360 months)

=

1200*[1-{(1+0.003958)-360}]/0.003958

=

1200*191.716538

=

$230,041

Maximum price of house

=

loan +downpayment

=

$77830+230,041

=

$307,871

The answer is option © $307,871

Note

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