The objectives of this section are to

- understand the difference between cash price and hire purchase
- be able to calculate percentage increase and decrease in price
- be able to calculate GCT in context.

You are familiar with buying items in shops and markets but often, when buying expensive goods, different methods of payment are available.

You might be offered a *hire purchase* agreement: you would pay a deposit and then pay the remainder of the cost of the item in a specified
number of (often monthly) instalments. In a *sale*, the cash price might be reduced.

You need to remember that most goods are subject to a government sales tax, often referred to as VAT (value added tax). In Jamaica this government tax is GCT (general consumption tax) which is currently charged at 16%.

The monthly water bill for domestic users is calculated from information shown in the table below.

Fixed charge | J$350 |

Charge per gallon | 20 cents |

Calculate the TOTAL amount of the bill for a month when a consumer used 3850 gallons.

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Total amount of bill | = J$350 + 3850 × J$0.20 |

= J$350 + J$770 | |

= J$1120 |

A printer is advertised for sale at J$84 000. A discount of 12% is given if it is bought for cash. It can also be bought on hire purchase by paying a deposit of J$29 400 followed by 24 monthly payments of J$2300 each. Calculate

the cash price,

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Cash price | = J$84 000 − 12% of J$84 000 |

= J$⎧ ⎨ ⎩ 84000 − × 84 000⎫ ⎬ ⎭ | |

= J$73920 |

**Note**: it is quicker to calculate the cash price as

88% of J$84 000 | = J$ ⎛ ⎝ × 84 000⎞ ⎠ |

= J$73 920 |

the hire purchase price,

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Hire purchase price | = J$29 400 + 24 × J$2300 |

= J$(29 400 + 55 200) | |

= J$84 600 |

the amount saved by buying the printer for cash rather than on hire purchase.

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Amount saved | = J$84 600 − J$73 920 |

= J$10 680 |

In selling an article, a shopkeeper made a profit of 20% on his cost price of J$8000. What was the selling price?

20% of J$8000 | = J$⎛ ⎝ × 8000⎞ ⎠ |

= J$1600 |

This is the shopkeeper's profit, so the selling price is

J$8000 + J$1600 = J$9600

*Note:* It is quicker to calculate

120% of cost price | = J$ × 8000 |

= J$9600 |

Calculate the TOTAL amount a customer pays for the television set.

ShowTotal amount paid | = $1600 + 15% of $1600 |

= $⎛ ⎝1600 + × 1600⎞ ⎠ | |

= $(1600 + 240) | |

= $1840 |

The sale price of $1600 is 20% LESS THAN the original price. Calculate the ORIGINAL price of the television set.

ShowIf the original price is $*p*, then

80% of p | = 1600 |

that is, × p | = 1600 |

p | = 1600 × |

= 2000 |

So the original price was $2000.

Check: 20% of $2000 | = × $2000 |

= $400 | |

So sale price | = $2000 − $400 |

= $1600, as expected. |