1. Problem: Calculate the actual after-tax cost of the furniture and the difference between your estimate and the actual after-tax cost. 2. Calculate the actual after-tax cost of the furniture: - Let the cash price be $P$ and the HST (tax) rate be $t$ (commonly 13% in Canada, i.e., $t=0.13$). - The after-tax cost is $$P_{after} = P + P \times t = P \times (1 + t).$$ - If the original price is not given, we cannot calculate the exact amount, but you can apply this formula once $P$ is known. 3. Calculate the difference between your estimate and the actual after-tax cost: - If your estimate was only the cash price $P$, then the difference is $$\text{difference} = P_{after} - P = P \times t.$$ 4. Problem: The store offers an instalment plan: 36 monthly payments of 49.99. 5. Why the monthly payment plan? - To make the furniture affordable by spreading costs over time. - Allows customers with limited upfront cash to buy the furniture. 6. Calculate how many years it will take to pay in full: - Number of months: 36 - Number of years: $$\frac{36}{12} = 3$$ years. 7. Why is each installment $49.99$ and not $50$? - To appear cheaper and more attractive to customers (psychological pricing). 8. Instalment plan definition: - A payment option allowing a customer to pay the total amount in smaller, regular payments over time. 9. Calculate total cost with the instalment plan: - Monthly payment: $49.99$ - Number of payments: 36 - Total cost: $$49.99 \times 36 = 1799.64.$$ 10. Recall the after-tax cash price (from #1), say $P_{after}$. 11. Calculate the difference (interest equivalent): - $$\text{difference} = 1799.64 - P_{after}.$$ - This difference is the extra amount paid for the convenience of instalments. 12. A used car costs $3999 plus HST; instalment plan includes $1000 down payment + $199 monthly for 2 years. 13. Calculate after-tax cash price: - HST rate $t = 0.13$ - After-tax price: $$3999 \times (1 + 0.13) = 3999 \times 1.13 = 4518.87.$$ 14. Number of monthly payments: - 2 years \times 12 months/year = 24 payments. 15. Calculate total cost of monthly payments: - Monthly payment $199$, Number of payments 24 - $$199 \times 24 = 4776.$$ Final answers: - Furniture after-tax cost: $P_{after} = P \times (1 + t)$ - Difference estimate vs actual: $P \times t$ - Instalment total cost: $1799.64$ - Instalment time: 3 years - Used car after-tax cash price: $4518.87$ - Used car monthly payments total: $4776$ - Number of used car payments: 24