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# Express Unit - Percentages

ercentages are everywhere! Newspapers and consumer programmes are

constantly talking in percentages and debating about the rising or falling

price of something or other, whether it's house prices or the price of food.

Understanding percentages is an important practical skill that can help you

to save money, manage your money and make your money go further.

But what does percentage mean?

Per cent means out of every hundred.

So a percentage is the number or amount of something as part of a 100;

and 100% is the whole thing.

So if 80% of the population own a car that means 80 out of every

hundred people own a car.

And if you have 100% of something that means you have the whole

amount.

Imagine you're booking a holiday for you and your family and you've

found a brilliant deal: two weeks in the sun in a self-catering

apartment for only £300.

But the company offering the deal wants you to pay a 50% deposit!

If the full price of the holiday is £300, how much will the 50%

deposit cost?

We know that 100% is the whole number, which is £300 in this case.

50% is half of 100%. To find half of a number you divide by 2.

£300 divided by 2 is £150. So 50% of £300 is £150.

Discounts and sales are often advertised in percentages, so you need to

understand them to know exactly how much money you're saving!

Take this pair of jeans, advertised as having *10% off the original price*.

To understand if you are getting value for money, you need to be able to work

out the **percentage decrease** or in other words how much you're saving.

Don't panic! It's not as complicated as it seems!

To work out a 10% discount you need to divide by 10, because 10 is one

tenth of a 100.

When you divide by 10 you **move all the numbers one place to the right leaving the decimal point where it is, like this.**

So the original price of £30 divided by 10 is £3.00, which means that

you'll save £3.00 if you buy this pair of jeans in the sale.

To work out how much the jeans will cost, you need to *take away* the

amount you're saving from the original price. So, £30 take away £3.00

equals £27. Not bad.

What if the shop decides to change the deal to 20% off?

Here's a good tip on how to find 20%: find 10% first and then double it,

multiply by 2.

We already know that 10% off this pair of jeans is £3.00, so 20% off

the jeans means you'd save £6.00!

£30.00 take away £6.00 equals £24.00. Bargain!

Apart from sales where prices decrease, how do you work out costs

when prices **increase?**

Imagine that your mobile phone charges have increased by 5%.

Your monthly bill is usually around £30.00, and you want to know

roughly how much more you will be paying per month. To work this

out you need to find 5% of £30.

5% is half of 10% ... so an easy way of finding 5% is to find 10%

and then divide by 2.

So 10% of

£30.00 is

£3.00

£3.00 divided by 2 is £1.50

To work out how much your monthly phone bill will cost, you need

to *add* the extra amount you will be charged for to original price.

So, £30 add £1.50 equals £31.50.

So your bill will now be around: £31.50

Let's take an example where you need to compare prices to find the

best deal. Imagine you always buy the same brand of toothpaste

each month, but this month a new brand catches your eye.

Your usual brand, Dentaclean, is on sale at £1.65. Bright White

Toothpaste costs £2, but is on special offer this week at 25% off.

Which one's the cheapest? Dentaclean at £1.65 per tube, or Bright

White at £2.00 with 25% off?

The first thing to do is check that they are the same weight so you

know you are comparing like for like... They are... So now you need

to find out how much Bright White costs after taking the 25% off.

Remember that 50% is half, and 25% is half of 50%.

So, a way of finding 25% is to find 50%, and then half again.

Half of £2.00 is £1.00

Half of £1.00 is 50p

So with 25% off you're saving 50 pence. Not bad!

So, £2.00 take away 50p equals £1.50.

This means Bright White costs £1.50 with the offer; while Dentaclean

costs £1.65. You're 15 pence better off if you go for the one on

offer - which is better than a kick in the teeth!

As you can see understanding percentages will come in handy when

shopping for everyday goods and services for you and your family.

But an understanding of percentages will also be an advantage when

shopping around for bigger, more long-term things, such as a mortgage

deal; a new car or a savings account. It can really help you get the best

deals on borrowing money and saving money.

This is when you'll probably come across the terms **APR** and **AER. **Maybe

you don't understand these terms; and that may put you off shopping

around for the best deal.

But don't let them scare you off - once you understand them, you'll be

able to make better decisions and make the most of your money.

**APR**, or Annual Percentage Rate, is to do with **loans** or **money you owe**...

It's the actual cost of borrowing money: how much *interest* the bank will

charge you on **the money you owe**.

This could be a loan you've taken out to buy a car; a mortgage; a bank

overdraft or a credit card maybe.

So, let's say your washing machine is on its last legs and you need to

borrow a hundred pounds to buy new one. You've spotted this loan

being advertised at 16.1% APR.

This means that at the end of the first year, if you haven't paid the

loan back, you will owe the £100 plus the 16.1% APR.

So how much will you owe if you take this loan out?

Well, 16.1% of £100 is the same as £16.10. So at the end of the first

year you'll owe £116.10. You're paying £16.10 to borrow the £100.

On the other hand, **AER**, or Annual Equivalent Rate, is the amount of

**money the bank will pay you**

*on your savings over a year.*

If you are in credit in your bank account, or if you have put money away in

a savings accounts, the bank will pay *you* the sum of the AER each year.

So, imagine that Great Aunt Nora left you £200 in her will and you'd

like to save it for a rainy day. You see a savings account advertised

at 6.0% AER.

How much money will you have in the savings account at the end of

the first year? Well, your £200 will have increased by the amount of

the AER, which in this case would be 6% of £200.

To find 6%, you could find 1% first and then multiply by 6.

To find out 1% you divide by 100, or simply move the

numbers *two* places across to the right. Like this:

£200.00

£2.00 (00)

1% of £200 is £2, and £2 multiplied by 6 is £12.00.

So, at the end of the first year, you will have the original £200 plus

your 6% interest of £12, which works out as £212.00 in the account.

**Summary**

Don't let percentages get the better of you.

Remember, there are techniques you can use to make life easier for

yourself. Practice these techniques...

- To find 50%, find half, or divide by 2.
- To find 25%, find half and half again.
- To find 75%, find 50% and 25% then add them together.
- To find 10%, divide by 10 or move the numbers one place to the right.
- To find 1%, divide by 100 or move the numbers two places to the right.
- To find 5%, find 10% then halve it.
- To find 20%, find 10% and double it...
- ...and also, don't be put off by jargon.

Remember, when borrowing or saving money, the APR or AER can

help you compare the different deals available.

When borrowing money, look out for low APR rates.

When looking to save money, look out for the AER and go for the

highest rate you can find.

There are always offers and sales just around the corner so hang on

to your wallet! Use your knowledge of percentages and shop around

for the best deal!