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Mathematics

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Answers

4 parts
a

\3900.00$

b

\300.00$

c

8.33%8.33\%

d

\4000.00$

Step-by-step solution

7 steps

Here's the solution for Question 1:

Part 1

Given information:
Down payment = $300.00 Number of monthly payments = 18
Monthly payment amount = $200.00 Cash price = $3600.00

Part a

\3900.00$

The hire purchase price

  1. Calculate the total amount paid in monthly installments.

    Total monthly payments=Number of monthly payments×Monthly payment amount\text{Total monthly payments} = \text{Number of monthly payments} \times \text{Monthly payment amount}

    Total monthly payments=18×$200.00=$3600.00\text{Total monthly payments} = 18 \times \$200.00 = \$3600.00

  2. Calculate the hire purchase price by adding the down payment to the total monthly payments.

    Hire purchase price=Down payment+Total monthly payments\text{Hire purchase price} = \text{Down payment} + \text{Total monthly payments}

    Hire purchase price=$300.00+$3600.00=$3900.00\text{Hire purchase price} = \$300.00 + \$3600.00 = \$3900.00 The hire purchase price is \boxed{\3900.00}$.

Part b

\300.00$

The interest charged

  1. Calculate the interest charged by subtracting the cash price from the hire purchase price.

    Interest charged=Hire purchase price−Cash price\text{Interest charged} = \text{Hire purchase price} - \text{Cash price}

    Interest charged=$3900.00−$3600.00=$300.00\text{Interest charged} = \$3900.00 - \$3600.00 = \$300.00 The interest charged is \boxed{\300.00}$.

Part c

8.33%8.33\%

The percentage interest charged

  1. Calculate the percentage interest charged using the interest charged and the cash price.

    Percentage interest charged=(Interest chargedCash price)×100%\text{Percentage interest charged} = \left( \frac{\text{Interest charged}}{\text{Cash price}} \right) \times 100\%

    Percentage interest charged=($300.00$3600.00)×100%\text{Percentage interest charged} = \left( \frac{\$300.00}{\$3600.00} \right) \times 100\%

  2. Perform the calculation.

    Percentage interest charged=112×100%≈8.333%\text{Percentage interest charged} = \frac{1}{12} \times 100\% \approx 8.333\%

    The percentage interest charged is 8.33%\boxed{8.33\%} (rounded to two decimal places).

Part d

\4000.00$

The advertised cash price of the tablet computer represents a discount of 10% of the original cash price. Calculate the original cash price.

  1. Let the original cash price be XX.

    The advertised cash price ($3600.00) is the original cash price minus a 10% discount.

    Advertised cash price=Original cash price−(Discount rate×Original cash price)\text{Advertised cash price} = \text{Original cash price} - (\text{Discount rate} \times \text{Original cash price})

    $3600.00=X−(0.10×X)\$3600.00 = X - (0.10 \times X) $3600.00=X(1−0.10)\$3600.00 = X(1 - 0.10) $3600.00=0.90X\$3600.00 = 0.90X

  2. Solve for XX.

    X=$3600.000.90X = \frac{\$3600.00}{0.90} X=$4000.00X = \$4000.00 The original cash price is \boxed{\4000.00}$.

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