Maths - Percentages

Jack McKinlay
Note by Jack McKinlay, updated more than 1 year ago
Jack McKinlay
Created by Jack McKinlay about 7 years ago
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SQA Maths Note on Maths - Percentages, created by Jack McKinlay on 08/23/2013.
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Calculations involving Percentages: Finding a percentage of a quantity: You will have to be able to use the basic skills of doing percentages for many different calculations in the exam.Most of these questions will be in a real life context. You will find further practice of percentages in some of the other number revision bites, using real life contexts.Percent means 'out of one hundred', so 15% means 15 out of one hundred.15% =  = 0.15 Example Find 30% of £800

Simple Interest: If you put money into a bank or building society they will pay you interest on this money.If you have borrowed money, from a bank or building society for a mortgage or other loan, you have to pay them interest.Simple interest is calculated on a yearly basis (annually) and depends on the interest rate. The rate is often given per annum (p.a.) which means per year. Example Sally deposits £600 into an account with an interest rate of 5% per annum.Calculate the interest that Sally receives in one year and find how much money she has in the account after one year.Interest = 5% of £600New balance = £600 + £30 = £630After one year Sally will have £630.

Simple Interest over multiple years: If money is left in a bank or building society for more than one year, then the amount of interest earned has to increase. Remember - this is simple interest. It is different from compound interest. Here's an example of how to calculate simple interest over multiple years. Example Darren leaves £350 in his building society account for 3 years. The account paid interest at a rate of 8% per annum. How much does he have in his account after 3 years?Interest for one year = 8% of £350Interest for three years = 3 x £28 = £84New balance = £350 + £84 = £434After three years Darren will have £434 in his account.

Simple Interest over a fraction of a year: If money is not left in a bank account for a whole year then only a fraction of the interest gets paid. Example Find the interest that Damon earns on £40 if he keeps it in the bank, paying 8.5% interest p.a., for 6 months.Interest for one year = 8.5% of £40You now know the interest for one year, so to find the interest per month, divide by 12 then multiply by the number of months.Interest for 1 month = £3.40 ÷ 12= £0.28333......Interest for 6 months = £0.28333..... x 6 = £1.70New balance = £40 + £1.70 = £41.70Damon will earn £1.70 in interest.

Compound Interest Compound Interest is similar to Simple interest in that the interest is added on annually. The difference between the two is that simple interest is a fixed amount of interest that is added on every year, whereas with compound interest the amount you are calculating interest on, changes every year. The interest is calculated for the 1st year and is then added on to the original amount to give you the amount after the 1st year. The interest for the 2nd year is then calculated from the amount after the 1st year, which then gives you a different amount of interest gained from the 1st year. Example Calculate the amount of compound interest Jane will have earned on £6000 at 2.8% for 3 years. Method 1 Year 1Amount after Year 1: £6000 + £168 = £6168Year 2Amount after Year 2: £6168 + £172.70 = £6340.70Year 3Amount after Year 3: £6340.70 + £177.54 = £6518.24Total amount of compound interest earned = £6518.24 - £6000= £518.24 Method 2 This is a much quicker methodAs the interest is going up by 2.8% p.a. this means that each year the amount is 102.8% of the previous year. Therefore:However, this only gives you the amount after year 1. To get the amount after year 3:Total amount of interest earned = £6518.24 - £6000 = £518.24

Appreciation/Depreciation: The value of a house is usually said to increase with time. Therefore its value is said to appreciate. Example A flat bought for £74 000 in 2005 appreciated in value each year by 1.5%.Calculate the value of the house after four years.The value of the flat after four years is £78 540.90.The value of a car however is usually said to decrease in value with time. Therefore its value is said to depreciate. Example Jack and Trisha bought a new car for £8500 in 2008. In the first year, its value depreciated by 20%, in the second year by 15% and in the third by 10%.Calculate the value of the car at the end of each year.Value at the end of Year 1:Percentage has gone down by 20%, therefore 100% - 20% = 80%Value at the end of Year 2:Percentage has gone down by 15%, therefore 100% - 15% = 85%Value at the end of Year 3:Percentage has gone down by 10%, therefore 100% - 10% = 90%

Percentages

Compound Interest

Appreciation/Depreciation

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