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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
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%
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
£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:
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.
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!