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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
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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