Percentages
. It is mostly denoted using the percent sign, % For example, 50% (read as “fifty percent”) is equal to 50/100, or 0.50. Percentages are similar to ratios, they’re used to express how large/small one quantity is relative to another.
PERCENTAGE GAIN
Example: A man invests £1,000 in the bank for 5 years earning 5% in interest per annum. How much will he have after five years?
Answer:
The man earns £1276.28 in 5 years.
Explanation:
Generally we will need to form a multiplier or formula which we’ll use to find out how much money the man would have after any years. To find the amount of money the man earns after 1 year you will first need to work out the percentage (5%) of what he invests at start and then add the 5% to the original investment, this will give you the amount of money he earns in the first year. If you work out 5% of £1,000 and add it to £1,000 you will get the amount of money the man will have in the first year. If you do the same for the amount of money you get for the first year you will get the amount of money the man gets in the second year. In the first year the man will receive:
There is a pattern in the sequence of money he receives each year and where there is a pattern a formula can be formed. Imagine having to work out how much he would earn after 20 years, this will take a very long time to work out. The quickest way is to find a multiplier or formula. The quickest way to find a percentage of a number and adding the percentage to the original number is converting the percentage into a decimal then adding it to 1 and multiplying it by the original value or number. For example; To find the amount of money the man earns in the first year. We would convert 5% into a decimal and adding it to 1 and then multiplying it by £1000. 1 gives you the original amount in the calculation and the 0.05 converted decimal adds on the 5%
£1050 is the amount of money the man receives in the first year…
Once the above step seems logical to you the following will be very simple. To find the amount of money for any asked year. You simply power the multiplier in this case 1.05 to the number of years. So find out how much the man earns in 5 years;
The following illustration shows how to workout such questions;
PERCENTAGE LOSS
The above was working out the percentage gain, here we shall workout the percentage loss in a situation.
Example: A man buys a car at £17,000. The car losses 8% due to old age and wear and tear (depreciation). How much is it worth after 3 years?
Answer
Explanation:
The question is different from the above question and the final answer should be less than the original amount(£17,000). In the above situation we understand that to find 5% of an amount and add it together we multiply 1.05 by the amount after converting the 5% into a decimal, but for the above we’re trying to find out the gain not loss. In this situation instead of adding the percentage to 1 we would subtract. So first convert the percentage in question and the subtract it from 1 and then multiply by the original amount to find the loss.
In this case the car would be worth; £13,237.70
FINDING THE ORIGINAL AMOUNT
In some cases you might want to know the original amount if the final amount has been provided.
Example: A TV costs £190 in a sale of 5% OFF. What did it cost before the sale?
Answer
Explanation: This is a little tricky to understand, First find the percentage of the final amount, so;
Since we multiply to find the final amount, we would simply reverse by dividing to find the original amount, so;
So the price before the sale was £200.
