The Problem:
Here is important information:
Part A:
You want to explore the costs of renting and buying a property that you're interested in during the year 2010. You have it narrowed down to a few homes in the same neighbourhood. All homes remain at the same value annually, and have a frontage of 50 feet. Each home will cost $15 000 for any additional costs. You can afford payments up to $875/month and have $19 000 saved as a down payment.
The bank gives you three amortization options:
15 years at 2.1%
20 years at 2.1%
25 years at 2.1%
Choose an amortization period you want and find the maximum value of the home that you can afford with that option.
Part B:
The municipal mill rate in the neighbourhood is 22.375 mills. There is an educational mill rate of 11.35 mills.
The following list is the municipalities planned local improvement costs for the next 25 years in that neighbourhood:
M2LE2 Hand-in Assignment Questions - 1
Boulevard reconstruction costs $4.25/foot
Water renewal costs $1.90/foot
Concrete street paving costs $2.65/foot
Land drainage system costs $6.10/foot
Find the total cost of the property taxes over the amortization period chosen.
Part C:
The rent for any home in the neighbourhood is 30% higher than the monthly mortgage payment for the first year. Rent will increase by 1.5% annually after that.
You can invest any money saved by renting in an account that pays 3.2%.
With the given information, compare the cost of buying and renting the home that fits your financial needs over the amortization period chosen. Then, make a final decision whether to rent or buy the home and give your most important reason for the decision.
1 mark for correct value of the house based on amortization period chosen
2 marks for work shown
1 mark for total property tax for the amortization period
3 marks for property tax calculations
1 mark for correct rent calculated
1 mark for total cost of buying home
1 mark for total cost of renting home
2 marks for conclusion with a valid reason
To solve this problem, we will go through each part one by one.
Part A: Choosing an amortization period
To find the maximum value of the home you can afford, you need to calculate your maximum monthly payment based on the given options and your financial situation. Let's calculate the maximum monthly payment for each amortization period:
For a 15-year amortization period:
Max monthly payment = $875
Interest rate = 2.1%
Using the formula for calculating the monthly mortgage payment, we can plug in the values to find the principal loan amount:
P = M * (1 - (1 + r)^(-n)) / r
Where P is the principal loan amount, M is the monthly payment, r is the monthly interest rate, and n is the total number of months.
In this case, we'll solve for P. Rearranging the formula, we get:
P = M * (1 - (1 + r)^(-n)) / r
P = $875 * (1 - (1 + 0.021) ^ (-15 * 12)) / 0.021
P = $147,664.61
For a 20-year amortization period:
Max monthly payment = $875
Interest rate = 2.1%
Using the same formula as before, we can calculate the principal loan amount for a 20-year amortization:
P = $875 * (1 - (1 + 0.021) ^ (-20 * 12)) / 0.021
P = $169,829.74
For a 25-year amortization period:
Max monthly payment = $875
Interest rate = 2.1%
Calculating the principal loan amount for a 25-year amortization:
P = $875 * (1 - (1 + 0.021) ^ (-25 * 12)) / 0.021
P = $186,814.91
Based on these calculations, you can afford a home with a maximum value of $147,664.61 for a 15-year amortization period, $169,829.74 for a 20-year amortization period, and $186,814.91 for a 25-year amortization period.
Part B: Calculating property taxes
To calculate the total cost of property taxes over the chosen amortization period, we need to calculate the annual property taxes first. Let's do that:
For the municipal mill rate:
Annual municipal property tax = (Property value * Mill rate) / 1000
Annual municipal property tax = (Property value * 22.375) / 1000
For the educational mill rate:
Annual educational property tax = (Property value * Mill rate) / 1000
Annual educational property tax = (Property value * 11.35) / 1000
To find the total property tax for the amortization period, we multiply the annual property tax by the amortization period in years.
Part C: Comparing buying and renting costs
To compare the cost of buying and renting the home over the amortization period, we need to calculate the total cost of buying and renting separately.
For buying a home:
- Calculate the monthly mortgage payment using the chosen amortization period and principal loan amount.
- Calculate the annual property tax based on the property value.
- Add up the monthly mortgage payments and annual property taxes for the amortization period.
For renting a home:
- Calculate the monthly rent for the first year based on the mortgage payment.
- Calculate the annual investment return on the money saved by renting and investing it in an account.
- Calculate the cost of renting for the amortization period by adding up the monthly rent and the annual investment return.
To make a final decision, compare the total cost of buying and the total cost of renting. Choose the option that results in a lower cost and provide a valid reason for your decision.
Please note that in order to provide you with numerical results and a valid conclusion, we need information on the property value you're interested in. With that information, we can proceed to calculate the costs and give a conclusion based on the comparison.
Part A:
To find the maximum value of the home that can be afforded with each amortization option, we need to calculate the monthly mortgage payment that can be made with the given information.
Let's start with the first amortization option:
Amortization period: 15 years
Interest rate: 2.1%
Monthly payment limit: $875
Using the loan amortization formula, the monthly mortgage payment can be calculated as follows:
P = Principal amount (maximum value of the home)
r = Monthly interest rate
n = Number of monthly payments
r = (2.1/100) / 12 = 0.00175 (monthly interest rate)
n = 15 * 12 = 180 (number of monthly payments)
875 = P * (0.00175 * (1 + 0.00175)^180) / ((1 + 0.00175)^180 - 1)
Now, solve for P:
P = 875 * ((1 + 0.00175)^180 - 1) / (0.00175 * (1 + 0.00175)^180)
Calculate this value to find the maximum value of the home.
Repeat this process for the remaining two amortization options (20 years and 25 years) to find the maximum values of the home that can be afforded with each option.
Part B:
To calculate the total cost of property taxes over the chosen amortization period, we need the mill rates and the costs for each local improvement project.
The total cost of property taxes can be calculated as follows:
Property tax = (Mill rate 1 + Mill rate 2) * (Property value + Boulevard reconstruction cost + Water renewal cost + Concrete street paving cost + Land drainage system cost)
Calculate this for each year of the amortization period and sum up the costs.
Part C:
To compare the cost of buying and renting the home, we need to calculate the total cost of buying the home and the total cost of renting the home over the chosen amortization period and compare them.
For buying, the total cost includes the down payment, monthly mortgage payments, and property taxes.
For renting, the total cost includes the rent for each year, adjusted for the annual increase, and the interest earned from investing the money saved by renting.
Compare these total costs and make a decision based on the lowest cost option.
Provide a final decision and the most important reason for the decision based on the calculated costs.