Produced by MEI on behalf of OCR © OCR 2013 Introduction to Quantitative Methods Reverse percentages

Produced by MEI on behalf of OCR © OCR 2013 Giving to charity Sometimes charities give the following information to people who want to give money. This is because charities can claim back the income tax that people have paid on their donations. But the basic rate of income tax is 20% so where does 25% come from? If you are a taxpayer, you can increase the value of your gift by 25% at no extra cost to yourself.

Produced by MEI on behalf of OCR © OCR 2013 Tax back for charity Suppose you decide to give £50 to charity. You had to earn more than £50 for you to have £50 left after the tax man took 20%. Tax has reduced your earnings by 20%; the multiplier for this is 0.8. Earnings  0.8 = £50. To work out how much you had to earn to be left with £50, do £50  0.8 = £ The charity can claim the tax back to get a total of £62.50.

Produced by MEI on behalf of OCR © OCR 2013 Percentage of what? You earned £62.50 You paid £12.50 tax You gave £50 to charity The charity gets the £12.50 tax too. £12.50 is 20% of £62.50 (what you earned) Check  £12.50 is 25% of £50 (what you gave) Check  50

Produced by MEI on behalf of OCR © OCR 2013 Who is comparing with what? The tax man compares the tax to the total amount earned (100%). The tax is 20%. The charity compares the tax to the amount given (100%). The tax is 25%.

Produced by MEI on behalf of OCR © OCR 2013 Reverse percentage calculations  multiplier  multiplier

Produced by MEI on behalf of OCR © OCR 2013 What was it before? A car is advertised at £6750 after a 10% discount. What was the price before the discount? The original price was multiplied by 0.9 to discount it by 10%  0.9

Produced by MEI on behalf of OCR © OCR 2013 What was it before? A car is advertised at £6750 after a 10% discount. What was the price before the discount? To find the original price divide £6750 by 0.9.  0.9  0.9

Produced by MEI on behalf of OCR © OCR 2013 The idea of present value Imagine you are running a business and you will be paid £3000 in a year’s time. If you had the money now, you could invest the money and get 5% interest in one year. The Present Value of £3000 in one year is less than £3000. Note that we are not thinking about inflation here, just that if you have the money now, you can use it to make more money.

Produced by MEI on behalf of OCR © OCR 2013 Working out present value Imagine you are running a business and you will be paid £3000 in a year’s time. If you had the money now, you could invest the money and get 5% interest in one year.  1.05