Shops and retailers look for way to encourage people to make purchases. This chapter will look at a couple of these different incentives, namely lay-by and discounts for paying cash.

Terms to remember

**Deposit:** an initial, partial payment for the cost of an item.

**Balance:** the amount owing after a deposit has been paid, i.e. $\text{cost }-\text{deposit }=\text{balance }$cost −deposit =balance .

**Interest:** an amount charged for loaning you the amount of the balance. Usually calculated as a percentage of the balancing owning using the compound interest formula.

**Repayment:** a fixed amount paid at regular time periods to pay back the balance.

## Paying Cash

A number of shops offer discounts to people who pay cash for their purchases. This is because cash, unlike other payment methods such as credit card, ensures the retailer receives the money straight away and without incurring any transaction fees. Most retailers offer a percentage off for paying cash. Click here if you need a refresher on calculating percentages.

#### Example

##### Question 1

Han purchases a drill selling for $\$400$$400 at a hardware store.

**A)** Calculate the amount he has to pay if he receives a trade discount of $7%$7%.

**B)** Calculate the amount he has to pay, to the nearest cent, if he pays with cash and receives a further discount of $10%$10%.

## Lay-By

Lay-by is a method of payment, where an initial deposit is made to secure an item for purchase and the balance is paid off at a later date, usually after a number of repayments. The initial deposit may be a fixed amount or a percentage of the total price.

#### Examples

##### Question 2

Maria purchased an item selling for $\$165$$165 on lay-by. If she paid a deposit of $\$16.00$$16.00, how much more did she have to pay, to the nearest cent, for ownership of the item to be transferred to her?

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##### Question 3

Maria purchased on lay-by an item valued at $\$180$$180. If she paid a deposit of $19%$19% and paid the balance off with fortnightly payments of $\$26$$26, how many fortnights are there until she receives ownership of the item? Round up your answer to the nearest integer.