Applied Math 40S May 13, 2008

3D Realty Handshake by flickr user lumaxart

Mortgages: Should I Buy or Rent?

http://www.forbes.com/2008/02/29/resale-value-autos-cars-forbeslife_cx_jm_0229resale_slide_2.html?partner=yahooca

http://tinyurl.com/3gplx7

The Dirksons Additional Costs to Purchase Their Home

The Dirksons live in Brandon and bought a house in Portage. They had the home appraised and paid $125.00 to have it done. The bank required a survey, and the cost of the survay was $300.00. the price of the home was $135 000.00, and since their down payment of $20 000.00 was less than 25% of the total price, they had to buy “High Ratio Mortgage Insurance” at a cost of 1.25% of the mortgage. The home insurance premium was $475.00 but they recieved a $150.00 rebate from the policy they had on their home in Brandon. The property taxes for the year had been paid by the previous owner, and so they owed 7 months of the total tax bill of $2 125.00. A dry-walling bill of $650.00 was split equally between themselves and the former owner. The Dirksons bought a used washer and dryer for $920.00. Moving expenses were $320.00 and legal fees that included the land transfer costs were $965.00.

The Dirksons Additional Costs to Purchase Their Home

The total additional costs are $5 957.08, or approximately $6 000.

If they do not have enough money set aside to cover these expenses, they might be able to add these costs into their mortgage.

A group of rural students is planning to go to university. One of the members of the group suggests that they purchase an older home rather than rent an apartment. After a careful analysis of their finances, the group decides that their gross monthly income would be around $3000.00. Monthly property taxes are estimated to be $125.00. Heating bills are estimated to be $150.00. The group can arrange a mortgage at a rate of 9%. The three members of the group are able to come up with a down payment of $8000.00. Determine the maximum affordable purchase price that can be considered if they take out a 25-year mortgage.

Total allowable monthly expenses on house0.32($3000) = $960Heating & Taxes$125 + $150 = $275

Maximum Possible Monthly Mortgage PMT$960 - $275 = $685

Maximum Affordable Purchase Price is$90 731.73

Most home buyers make monthly payments, but it is also possible to make payments twice a month, every two weeks, or every week. The amount of the payment is determined by the following:

• the principal of the mortgage (the size of the loan)

• the amortization term (the number of years you have to repay the mortgage)

• the interest rate

Canadian Mortgages

It is important to use a loan calculator that calculates Canadian mortgage payments, because for Canadian mortgages the interest is compounded every six months, and this may not be the case for mortgages in other countries.

The Mortgage Centrehttp://www.mortgagecentre.com/index.cfm

The Jamison's MortgageThe Jamison family has decided to buy a house. they will require a $121 000.00 mortgage to help pay for the house.

• Bank A offers them a 25 year mortgage at 7.25%. Determine the size of the monthly payment, the total amount paid for the mortgage, and the total amount of interest paid when the mortgage is repaid.

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• Bank B offers them a 20 year mortgage at 7.25%. Determine the size of the monthly payment, the total amount paid for the mortgage, and the total amount of interest paid when the mortgage is repaid if they repay the mortgage with monthly payments over 20 years.

The Jamison's Mortgage• How much interest do they save by repaying the mortgage in 20 years instead of 25 years?

The Jamison's Mortgage

• Bank C offers them a 25 year mortgage at 7.00%. Determine the size of the monthly payment, the total amount paid for the mortgage, and the total amount of interest paid when the mortgage is repaid.


The Jamison's Mortgage• How much interest do they save by paying the mortgage in 25 years at 7.00% instead of in 25 years at 7.25%. (i.e. how much cheaper is Bank C than bank A?)

Buying vrs. Renting

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




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%

HOMEWORK


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


$6 000.00

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$9 413.87 ∑Prn(1,36) = -5312.04

$11 312.04

HOMEWORK

Business

Applied Math 40S May 13, 2008