Calculate the deposit as a percentage of the cash price.
Understand the Problem
The question asks to calculate the deposit paid for a television as a percentage of its cash price, using the total hire-purchase price, which includes a deposit and monthly payments.
Answer
The deposit as a percentage of the cash price is approximately \(20\%\).
Answer for screen readers
The deposit as a percentage of the cash price is approximately (20%).
Steps to Solve
- Calculate the Total Monthly Payments
First, we need to calculate the total of the monthly payments for the television. Since there are 12 monthly payments of $113, we calculate:
[ \text{Total Monthly Payments} = 12 \times 113 = 1356 ]
- Calculate the Deposit Amount
Next, we find the deposit amount by subtracting the total monthly payments from the hire-purchase price. The hire-purchase price is $1651:
[ \text{Deposit} = \text{Hire-Purchase Price} - \text{Total Monthly Payments} ]
Substituting the values:
[ \text{Deposit} = 1651 - 1356 = 295 ]
- Calculate the Deposit as a Percentage of the Cash Price
Now, we can calculate the deposit as a percentage of the cash price, which is $1475. The formula to calculate the percentage is:
[ \text{Percentage} = \left( \frac{\text{Deposit}}{\text{Cash Price}} \right) \times 100 ]
Substituting in our values:
[ \text{Percentage} = \left( \frac{295}{1475} \right) \times 100 \approx 20 ]
The deposit as a percentage of the cash price is approximately (20%).
More Information
The deposit paid for the television is a significant portion of its cash price, highlighting how hire-purchase agreements can involve sizable upfront costs. Understanding this helps consumers make informed buying decisions.
Tips
- Miscalculating total monthly payments by forgetting to multiply the monthly payment by the number of months.
- Confusing the hire-purchase price with the cash price which can lead to incorrect deposit calculations.
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