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1) The Tremblays have been preapproved by their bank to enter the housing market with a mortgage interest rate of 8

Finance Dec 21, 2020

1) The Tremblays have been preapproved by their bank to enter the housing market with a mortgage interest rate of 8.6%. They have $30,000 set aside for a down payment. They have also calculated that they can afford a monthly payment of $1,350. They have narrowed their search to three houses and are hoping that financial constraints will narrow their choices. The three houses will cost the following amounts: $150,000, $270,000, and $400,000. The bank will add $50 to each mortgage payment if they put less than 20% down and an additional fee of $50 more to each payment if they put less than 10% down (Total 5 marks) a. Which of these houses can they afford with a 30-year mortgage? (2 marks) b. Which of these houses can they afford with a 15-year mortgage? (2 marks) I c. Which house do you think they should buy? (1 mark)
2. The Young household is looking at buying a house. The three houses they are looking at cost the following: $160,000, $190,000 and $210,000. They can pay up to $900 in monthly mortgage payments. They currently have $18,000 set aside for a down payment. Similarly to the Tremblay's bank, the Youngs' bank will add $40 to each mortgage payment if they put less than 20% down and an additional fee of $30 more to each payment if they put less than 10% down. (Total 5 marks) a. Which of these houses can they afford with a 30-year mortgage at an interest rate of 3.5%? (2 marks) b. Which of these houses can they afford with a 15-year mortgage at an interest rate of 2.8%? (2 marks) c. Which house do you think they should buy? (1 mark)

Expert Solution

Q1 Tremblays      
       
  House 1 House 1 House 1
Price 150000 270000 400000
DP 30000 30000 30000
Amount to be financed 120000 240000 370000
DP / Price 20 11.111111 7.5
       
Rate p.m. (8.6% p.a.)   0.0071667  
       
30 year instalment 931.21406 1862.4281 2871.2433
Extra payment   50 100
Monthly instalment 931.21406 1912.4281 2971.2433
       
15 year instalment 1188.7321 2377.4642 3665.2572
Extra payment   50 100
Monthly instalment 1188.7321 2427.4642 3765.2572

a) Tremblays can afford house 1 (Price $150,000) under a 30 year mortgage as instalment is $931,21 which is lower than $ 1350.

b) Tremblays can afford house 1 (Price $150,000) under a 15 year mortgage as instalment is $1188.73 which is lower than $ 1350.

c) Tremblays should by house 1 (Price $ 150,000)

Q2 Young Household      
       
  House 1 House 1 House 1
Price 160000 190000 210000
Down payment 18000 18000 18000
Amount to be financed 142000 172000 192000
DP / Price 11.25 9.4736842 8.5714286
       
Rate p.m. (3.5% p.a.)   0.0029167  
       
30 year instalment 637.64346 772.35686 862.1658
Extra payment 40 70 70
Monthly instalment 677.64346 842.35686 932.1658
       
Rate p.m. (2.8 p.a.)   0.0023333  
       
15 year instalment 967.02489 1171.3259 1307.5266
Extra payment 40 70 70
Monthly instalment 1007.0249 1241.3259 1377.5266

a) Young Household can afford House 1 (Price $ 160,000) and House 2 (Price $ 190,000) under a 30 year mortgage with interest rate 3.5% as the instalments are $ 677.64 and $ 842.36 respectively which are lower than $ 900.

b) Young Household cannot afford any house under a 15 year mortgage with interest rate 2.8% as the instalments of the three houses are $1007.02, $1241.33 and $1377.53 respectively which are all higher than $ 900.

c) They should buy house 1 (price $ 160,000) under a 30 year mortgage as the interest rate is lower.

Note: to calculate EMI, the following function can be used in excel:

=pmt (rate per month, no. of payments i.e. 12 * 30 or 15, present value i.e. amount to be financed).

In absence of excel, it can be calculated by discounting (1 + monthly interest rate) a total of 12 * 30 or 15 times and summing the results (can use GT function in a calculator for this) .

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