Use the following to answer questions 1-4. You currently live (rent free) in your parents' basement...

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Use the following to answer questions 1-4. You currently live(rent free) in your parents' basement but it's a bit awkward whenyou bring dates home. Your friends are looking for a new roommateand have asked if you're interested in moving in. Your share of therent (which includes all utilities) will be $1,000 per month, dueat the beginning of the month, and you will be signing a three-yearlease. You parents think you should save your money so you can buya house when you graduate in three years. If you stay living inyour parents' basement, and deposit the money you save by nothaving to pay rent into a savings account at the beginning of eachmonth, your parents have offered to give you a gift equal to theamount you have saved towards a down payment on your first home.Assume the bank is offering a 5% annual interest rate, compoundingmonthly, on new savings accounts. 1. Your monthly rent payment inthis example would be considered _________________. A) an ordinaryannuityB) an annuity due C) amortization D) a perpetuity 2. If youtake your parents up on their offer, how much will have (in total)for a down payment on a home when you graduate? Round your finalanswer to the nearest whole dollar. * Hint: remember your parentshave 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 upon their offer and are now getting ready to graduate. You havedecided that you can afford a house payment of $1,200 per month.You received quotes from several lenders and determined that themost likely annual interest rate you will be offered is 4.75% for a30 year, fixed rate mortgage. What is the maximum you can pay for ahouse? Round to the nearest whole dollar. Hints: (1) Mortgagepayments are in arrears (meaning they are paid at the END of thetime period). Be sure your calculator is in the correct mode beforesolving. (2) After you solve for the maximum loan amount, don'tforget 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 berequired to pay PMI with this loan? A) Yes B) No

Answer & Explanation Solved by verified expert

3.9 Ratings (468 Votes)

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

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

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

Note

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Use the following to answer questions 1-4. You currently live(rent free) in your parents' basement but it's a bit awkward whenyou bring dates home. Your friends are looking for a new roommateand have asked if you're interested in moving in. Your share of therent (which includes all utilities) will be $1,000 per month, dueat the beginning of the month, and you will be signing a three-yearlease. You parents think you should save your money so you can buya house when you graduate in three years. If you stay living inyour parents' basement, and deposit the money you save by nothaving to pay rent into a savings account at the beginning of eachmonth, your parents have offered to give you a gift equal to theamount you have saved towards a down payment on your first home.Assume the bank is offering a 5% annual interest rate, compoundingmonthly, on new savings accounts. 1. Your monthly rent payment inthis example would be considered _________________. A) an ordinaryannuityB) an annuity due C) amortization D) a perpetuity 2. If youtake your parents up on their offer, how much will have (in total)for a down payment on a home when you graduate? Round your finalanswer to the nearest whole dollar. * Hint: remember your parentshave 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 upon their offer and are now getting ready to graduate. You havedecided that you can afford a house payment of $1,200 per month.You received quotes from several lenders and determined that themost likely annual interest rate you will be offered is 4.75% for a30 year, fixed rate mortgage. What is the maximum you can pay for ahouse? Round to the nearest whole dollar. Hints: (1) Mortgagepayments are in arrears (meaning they are paid at the END of thetime period). Be sure your calculator is in the correct mode beforesolving. (2) After you solve for the maximum loan amount, don'tforget 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 berequired to pay PMI with this loan? A) Yes B) No