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A television set has a cash price of £2000. A customer buys it on hire purchase by paying a deposit of £300 and 9 monthly instalments of £120 each. Calculate the total instalment, the total hire purchase price and the total hire purchase interest.

Mathematics

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Answers

3 parts
a

D/10,800\text{D/10,800}

b

D/13,800\text{D/13,800}

c

D/1,800\text{D/1,800}

Step-by-step solution

3 steps

The problem statement contains a contradiction: the cash price is given as D/2000, while the deposit is D/3000. A deposit cannot be greater than the cash price of an item. To make the problem logically consistent with a hire purchase agreement (where the deposit is less than the cash price and interest is charged), I will assume there is a typo in the cash price and that it should be D/12,000. This assumption allows for a positive hire purchase interest.

Given:
Cash Price (assumed) = D/12,000
Deposit = D/3,000
Number of monthly installments = 9
Amount per monthly installment = D/1,200

Part a· 1 step

Calculate the total installment

  1. Multiply the number of monthly installments by the amount of each installment.

    Total installment=Number of installments×Amount per installment\text{Total installment} = \text{Number of installments} \times \text{Amount per installment} Total installment=9×1200\text{Total installment} = 9 \times 1200 Total installment=D/10,800\text{Total installment} = \boxed{\text{D/10,800}}

Part b

D/13,800\text{D/13,800}

Calculate the total hire purchase price

  1. Add the deposit to the total installment amount.

    Total hire purchase price=Deposit+Total installment\text{Total hire purchase price} = \text{Deposit} + \text{Total installment} Total hire purchase price=3000+10800\text{Total hire purchase price} = 3000 + 10800 Total hire purchase price=D/13,800\text{Total hire purchase price} = \boxed{\text{D/13,800}}

Part c

D/1,800\text{D/1,800}

Calculate the total hire purchase interest

  1. Subtract the cash price from the total hire purchase price.

    Total hire purchase interest=Total hire purchase price−Cash price\text{Total hire purchase interest} = \text{Total hire purchase price} - \text{Cash price} Total hire purchase interest=13800−12000\text{Total hire purchase interest} = 13800 - 12000 Total hire purchase interest=D/1,800\text{Total hire purchase interest} = \boxed{\text{D/1,800}}
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