Practical Math Problems for Finance and Geometry

Property Tax and Assessment Calculations

A home has an assessed value of $430,000.

Calculating Portioned Assessment

Calculate the total portioned assessment for the property if the portioned percentage is 45%:

• $430,000 × 0.45 = $193,500

Municipal and Education Tax

The mill rate for the Municipal tax is 24 mills on the portioned assessment:

• $193,500 × (24 / 1,000) = $4,644

In addition to the Municipal tax, there is an Education tax of $3,870 and a provincial tax credit of $700. The total tax calculation is:

• $4,644 + $3,870 - $700 = $7,814

Calculating Gross Debt Service Ratio (GDSR)

George is considering purchasing a home. He earns a gross income of $44,400 annually. His monthly costs include:

• Heating: $140
• Property Taxes: $200
• Mortgage Payment: $940

To calculate George’s Gross Debt Service Ratio (GDSR), we first find his monthly gross income ($44,400 / 12 = $3,700):

• GDSR = ($140 + $200 + $940) / $3,700 = 0.35

Mortgage Financing and Interest Costs

Jing-Wei is purchasing a home for $310,000 with a down payment of 5%. She will finance the mortgage over 25 years.

Amount Borrowed

• $310,000 × 0.95 = $294,500

Monthly Mortgage Payment

If the cost is $5.26 per month for each $1,000 borrowed:

• ($294,500 / 1,000) × 5.26 = $1,549.07

Total Cost of Financing

Calculate the interest paid over the 25-year mortgage:

• Total paid: $1,549.07 × 12 × 25 = $464,721
• Interest: $464,721 - $294,500 = $170,221

Vehicle Financing and Purchase Costs

Van Financing

Melanie purchased a van for $8,000 (after taxes) with a $1,500 down payment. The remaining balance is $6,500. The bank offers an annual interest rate of 7% over 5 years.

Interest on the first month’s payment:

• $6,500 × 0.07 × (1 / 12) = $37.92

Used Car Purchase

Maya is purchasing a used car from a dealership for $3,500 before taxes. Her trade-in value is $500.

Total amount after 13% taxes:

• Pre-tax amount: $3,500 - $500 = $3,000
• Total: $3,000 × 1.13 = $3,390

Private Vehicle Purchase

Odette is purchasing a vehicle privately. Additional costs include a safety inspection ($40) and a lien search ($15). Note: The lien search is not taxed.

• Total: ($40 × 1.05) + $15

Car Insurance and Depreciation

Lowering Insurance Costs

Two changes to lower the total cost of car insurance include:

• Making payments upfront rather than in multiple installments.
• Increasing the deductible.

Vehicle Depreciation

Chris purchases a snowmobile for $11,500. It depreciates at a rate of 15% per year.

• Depreciation after 1 year: $11,500 × 0.15 = $1,725
• Remaining value: $9,775

Geometry and Trigonometry Applications

Distance to the Leaning Tower of Pisa

Mario is 20 m away from the tower, which is 56.67 m tall and leans at an angle of 4° from the vertical (creating a 94° angle with the ground).

Using the Law of Cosines (a² = b² + c² - 2bc cosA):

• 20² + 56.67² - (2 × 20 × 56.67 × cos(94°))
• √3769.61 = 61.4 m

Octagon Central Angles

Juanita is building a regular octagon table. To find the measure of one central angle:

• 360° / 8 = 45°

Measurement Tolerance and Statistics

Minimum Value in Measurement

Given the measurement 2.5 mL ^{+0.3 mL}_-0, the minimum value is:

• 2.5 mL

Percentile Ranking Formula

The formula for percentile ranking (PR) is:

• PR = (Number of people below / Total number of people) × 100