Installment Plan
1. **State the problem:** Calculate the total cost using instalment plan and compare with after-tax cash price for furniture, then analyze the cost and payments for a used car.
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2. **Calculate total cost for sofa and love seat using instalment plan:**
Let the monthly instalment be $P$ and the number of months $n$.
Since the HST is included in instalments, total cost is simply $P \times n$ plus down payment if any.
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3. **Recall after-tax cash price for furniture from #1:**
Suppose cash price before tax is $C$, tax rate is $t$, after-tax price is $C (1 + t)$.
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4. **Calculate difference:**
Difference $= \text{Total instalment cost} - \text{After-tax cash price}$
This represents the interest paid on the loan.
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5. **Calculate after-tax cash price of the car:**
Cash price $= 3999$
Assuming HST = 13% = 0.13,
After-tax price $= 3999 \times (1 + 0.13) = 3999 \times 1.13 = 4518.87$
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6. **Calculate how many monthly payments to pay loan in full:**
Down payment $= 1000$
Monthly payment $= 199$
Loan balance after down payment $= 4518.87 - 1000 = 3518.87$
Number of payments needed $= \lceil \frac{3518.87}{199} \rceil = \lceil 17.68 \rceil = 18$ months
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7. **Calculate total cost of monthly payments:**
Total monthly payments $= 199 \times 18 = 3582$
**Final answers:**
- After-tax cash price of car: $4518.87$
- Number of monthly payments: 18
- Total cost of monthly payments: $3582$
Note: The problem's furniture prices and instalment amounts are not specified; these steps guide you how to calculate given data.