Applied Math 40S May 14, 2008

It's a little more complicated nowadays ...Buy or Rent?

Mortgage by flickr user Rev Dan Catt

1894

The Petri family needs to move, and so they are looking for another home. They are considering buying or renting a home. The price of a suitable home is $125 000. The cost of renting a similar home is $875 per month. They have $21 000 invested in an account that is growing by 7% per year, and they will use this for the down payment and to cover the 'Additional Costs when Purchasing a Home' if they buy. They have also checked with their bank about a mortgage, and they can get a 25-year mortgage at 7.25% to pay for the balance of the home. Other things to consider are:

• the 'Additional Costs when Purchasing a Home' are $6000.00, and so they will have $15 000 for the down payment• annual property taxes are about 1.5% of the value of the home• the home is expected to appreciate at 4% per year• rental payments are also expected to increase 4% per year• they expect to receive 7% per year growth in their investment if they do not use the $21 000 as a down payment for the home.

The Petri Family: A Buy vrs. Rent Case Study

1. What is the amount of the monthly mortgage payment?


$787.51

N=I%=PV=PMT=FV=P/Y=C/Y=PMT: END BEGIN



2. If the property taxes are 1.5% of the market value, how much are property taxes the year they buy the home? After they own the home for 10 years?

$1 875.00$2 775.46

HOMEWORK


3. What percent of the first mortgage payment is used to pay interest?

83.14%

∑Int(1,1) = -654.76

HOMEWORK


4. (a) How much is left owing on the home after one year (i.e. 12 payments)?

(b) What is the total amount they have paid in mortgage payments in one year?

(c) How much was the mortgage reduced after 12 payments?

(d) What percent of the money paid in the first year was used to reduce the principal of the mortgage?

bal(12) = 108 353.83

12 x $787.51 = $9 450.12

∑Prn(1,12) = -1646.17

17.42%

HOMEWORKN=I%=PV=PMT=FV=P/Y=C/Y=PMT: END BEGIN


5. If the market value of the home increases 4% per year, what is the value of the home after 10 years?

$125 000 x 1.04 = $185 030.5410

HOMEWORK


6. If they rented the home for one year at $875 per month, how much would they pay for the year?

How much would the annual rental charge be for the 10th year they rent if rental rates increase 4% per year.

$10 500.00

$875 x 1.04 = $1 295.2110

HOMEWORK


7. If they rent the house and invest the $21 000 at 7% per year, how large would the investment be after 10 years?

$42 202.89

HOMEWORK



$15 000.00

8. What equity does the Petri family have in the home immediately after buying it?

Equity = Purchase Price(*) - Mortgage Principal Remaining

After 2 years?

After 3 years?

∑Prn(1,24) = -3413.87$18 413.87

∑Prn(1,36) = -5312.04$20 312.04

HOMEWORK


9. How do the mortgage payments and rental payments compare during the first year? After 5 years? After 10 years?

The Petri Family: A Buy vrs. Rent Case Study10. How do the total costs of mortgage payments and rental payments compare after 1 year?


10. How do the total costs of mortgage payments and rental payments compare after 2 years?


10. How do the total costs of mortgage payments and rental payments compare after 10 years?

The Browns have an opportunity to buy a home valued at $50 000 with a down payment of $5000 and a mortgage of $45 000, or rent the home for $525 per month.

Rent or Buy? A Case Study ...

If they rent, their rental payments will increase by 3% each year, and they expect to get a 7% annual return on their investment of the $5000 they did not use as a down payment.

If they buy, they will get a 15-year mortgage at 7.5%. Annual property taxes are approximately 1.5% of the market value (i.e. the sale price) of the home. They expect their home to appreciate in value by about 2% per year. (That is, it will become 2% MORE VALUABLE each year. If it is worth $100 this year, next year it will be worth $102 and the year after that it would be worth $104.04.)

(a) What is the size of the monthly mortgage payment?

(b) What will their equity be in the home after 2 years of ownership? 10 years?


(c) After one year, how does the cost of payments plus property taxes compare with the cost of rental payments?

(d) After 10 years, how does the annual cost of payments plus property taxes compare with the annual cost of rental payments?

(f) What is the net cost of owning the home (Mortgage, down payment, add. costs, taxes, equity) for 10 years? Of renting (rent and investment returns) for 10 years?

(e) What might be two reasons for the Brown family to rent instead of buy - even though renting seems to be more expensive in the long run?

(d) After 10 years, how does the annual cost of payments plus property taxes compare with the annual cost of rental payments?






Mr. T’s family has decided to buy a larger home, and the date of possession is April 1.

The price of the home is $135 000, and he has $45 000 as a down payment. He will buy homeowners insurance on the new home for $425, but will receive a refund of $300 from his previous home insurance policy. He has the new home appraised by a real estate agent, and the fee is $250. The bank requires a land survey which costs $550. His legal fees, including land transfer taxes and disbursements, are $875.The movers charged $1200 for moving his furniture and other belongings, and the company he works for paid half of this. The family decided to install new carpets into part of the house at a cost of $2400 plus PST and GST (7% each). He did the installation himself, and so there were no installation charges. They also bought a new fridge for $940 plus PST and GST (7% each) to replace the old one that did not fit into the new kitchen. The previous owner had paid the property taxes of $2350 for the period January 1 to December 31, and he had to pay for his share of the taxes. The cost of hooking up telephone and TV are $45.Determine the additional costs of moving for Mr. T and his family.

HOMEWORK

Ms. Johnston has decided to buy a home. She requires a $65 000 mortgage. The mortgage interest rate is 7.75%, and she will repay the mortgage with monthly payments. She needs to decide whether she will select a 20- or 15-year amortization term. How much do her monthly payments increase, and how much money will she save if she chooses a 15-year term instead of a 20-year term? Would you advise Ms. Johnston to get a 15- or 20-year mortgage? Why?

HOMEWORK

T. Bekka needs a $105 000 mortgage which he will repay with monthly payments in 25 years. The first bank he visits offers a mortgage at 8.5%, and the second bank at 7.9%.1. How much does he save each month if he takes the second offer?

2. How much does he save over the life of the mortgage if he takes the second offer?

HOMEWORK

Economy & Finance

Applied Math 40S May 14, 2008