Navigating the Home Buying Process: A Mathematical Journey

Categories: Math

Introduction

Buying a home is generally viewed as one of the big stepping stones in someone’s life. The enthusiasm of buying your first home can be tempered with all of the different aspects that come with this purchase. These aspects can range from researching different places to live; to determining which mortgage scenario would work for you; to closing costs; land transfer taxes; and calculating ratios to determine if you are even eligible for a mortgage. This assignment has you working through some of the various areas of the home buying experience.

Follow the directions given for each of the different questions in order to correctly answer them. Read the instructions carefully to ensure that you correctly cover everything that is being asked of you in each question.

Selection of Residential Property

For this scenario, a mobile home located in West Woodbridge, Toronto, Ontario, was chosen. The property was selected due to its affordability, adequate space for sharing, and proximity to college, priced at $99,000. These factors make it an attractive option for a first-time homebuyer with specific needs and preferences.

Financial Calculations and Mortgage Scenarios

Down Payment and Mortgage Requirements

A 20% down payment on this property would amount to $19,800, reducing the mortgage requirement to $79,200. Opting for a 5% down payment would necessitate a high-ratio mortgage due to the lower initial payment.

Mortgage Scenario Analysis

Using the specified mortgage calculator, four different mortgage scenarios were analyzed, showcasing the impact of interest rates, amortization periods, and payment frequencies on the total cost and interest paid over the life of the mortgage.

Scenario Outcomes:

Interest Rate Amortization Period (Years) Payment Frequency Mortgage Payment Total Interest Paid Total Cost of House
3% 25 Monthly $79,200 $33,243.13 $112,443.13
4% 25 Monthly $79,200 $45,782.40 $124,982.40
3% 20 Monthly $79,200 $26,041.20 $105,241.20
3% 20 Biweekly $79,200 $25,989.80 $105,189.80

Insights from the Analysis:

  • The interest rate significantly affects the total interest paid, with a 1% increase resulting in an additional $12,539.27 over the life of the mortgage.
  • Shortening the amortization period from 25 to 20 years at a 3% interest rate reduces the total interest by $19,741.2.
  • Switching from monthly to biweekly payments further reduces the interest by $51.4, showcasing the benefits of more frequent payments.

Additional Costs:

Apart from the mortgage, potential homebuyers must account for additional costs such as legal fees, moving costs, and land registration fees.

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The land transfer tax for this property amounts to $1,430.00, adding to the overall cost of purchase.

Banks and mortgage lenders will need to determine if you can continuously and successfully pay a mortgage payment before they provide you with a mortgage for your property. The two ratios used to determine if you may be able to carry this debt are the GDS (gross debt service) and TDS (total debt service) ratios. Calculate the gross debt service (GDS) and the total debt service (TDS) ratios for the following data. The formulas for these ratios can be found in the Content information for this unit and in the textbook. (3 marks for each calculation: 1 mark for showing and using the correct formula, 1 mark for using the correct information in the formula and 1 mark for the correct percentage.)

Monthly mortgage payment $1,200 Personal loan payment $100

Property taxes $150 Car loan payment $400

Heating costs $300 Credit card payment $100

Gross monthly household income $5600

(a) the gross debt service (GDS) ratio (3)

Answer:

GDS = [(Monthly mortgage payment + taxes + heating)/ Gross monthly household income] X 100

= [(1200 + 150 + 300) / 5,600] X 100

= [1650 / 5600] X 100

= [0.2946] X 100

= 29.46 %

(b) total debt service (TDS) ratio (3)

Answer:

GDS = [(Monthly mortgage payment + taxes + heating+ debt payment)/ Gross monthly household income] X 100

= [(1200 + 150 + 300 + 100 + 400 + 100) / 5,600] X 100

= [2250/5600] X 100

= [0.4017] X 100

= 40.17%

Debt Ratios and Mortgage Eligibility

The Gross Debt Service (GDS) and Total Debt Service (TDS) ratios were calculated to assess mortgage eligibility, resulting in 29.46% and 40.17%, respectively. While the GDS ratio falls within acceptable limits, the TDS ratio exceeds the conventional threshold, potentially impacting mortgage qualification.

Conclusion

The home buying process is fraught with financial considerations, from down payments and mortgages to closing costs and debt ratios. Through careful analysis and planning, potential homebuyers can navigate these complexities, making informed decisions that align with their financial capabilities and housing needs. This exploration emphasizes the importance of understanding mortgage scenarios, additional costs, and debt service ratios in the context of purchasing a home, providing valuable insights for anyone embarking on this significant life journey.

Updated: Feb 21, 2024
Cite this page

Navigating the Home Buying Process: A Mathematical Journey. (2024, Feb 21). Retrieved from https://studymoose.com/document/navigating-the-home-buying-process-a-mathematical-journey

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