Percentages

Hong Kong

Stage 1 - Stage 3

Lesson

Shops, retailers and even financial institutions look for ways to encourage people to make purchases. Shops may offer incentives, such as offering lay-by services or discounts for paying cash, which we learnt about earlier. Allowing people to pay using credit cards is another way that encourages people to buy, as they can still purchase items even if they don't have the money to buy an item right there and then. Let's discuss these different payment methods in more detail.

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. However, it could also be calculated using the simple interest formula.

Credit cards allow people to basically "borrow" a continuing amount of money from the bank, which they have to repay within a certain period of time before they are charged interest (additional money as a fee for borrowing their money and not repaying it on time). Since the level of debt among teenagers is rising at an alarming rate, it is important that we understand how credit cards work and how interest is calculated because we don't want to end up in debt and have to repay a huge amount of money!

Through using a credit card, Mae incurs an interest charge of $11%$11% per month on the amount owing during each month. If she owed $\$220$$220, $\$980$$980, $\$270$$270 and $\$360$$360 during the last four months respectively, what was the total amount of interest she accrued over this period to the nearest cent?

**Think:** What is the total amount she will pay interest on?

**Do:**

Total | $=$= | $220+980+270+360$220+980+270+360 |

$=$= | $\$1830$$1830 | |

Interest | $=$= | $1830\times11%$1830×11% |

$=$= | $\$201.30$$201.30 |

Mae accrued $\$201.30$$201.30 over the four month period.

A number of large retailers allow you to purchase items *on terms*. "Terms" are specific conditions, such as the number and value of the repayments that need to be made, that a shop specifies for allowing you to pay off an item over an extended period of time. When you pay on terms, you normally end up paying a little bit more than you would if you can pay the full amount upfront, like you normally do for smaller purchases. However, it can be helpful, as it allows you to pay the amount off in smaller installments so you don't need to save up huge amounts of cash in one go.

If you use finance to buy an item, you are essentially taking out a loan from a financial or credit institution to pay for it. This means that you will have to pay interest on the amount you borrowed until the full amount is paid back. The longer it takes you to pay back the loan, the more interest you will have to pay.

Han purchased a fridge, valued at $\$702$$702, on terms. He paid a $6%$6% deposit, followed by monthly instalments of $\$21$$21 over $3$3 years.

How much did Han pay as the deposit?

Write your answer to the nearest cent.

What was the balance owing after he paid the deposit?

Write your answer to the nearest cent.

How much in total did he pay in instalments?

Write your answer to the nearest cent.

How much did he pay for the fridge altogether?

Write your answer to the nearest cent.

How much interest did he pay?

Write your answer to the nearest cent.

What was the interest charged as a percentage of the cost of the fridge? Write your answer as a percentage to two decimal places.

What was the annual rate of simple interest charged for buying on terms?

Write your answer as a percentage to two decimal places.