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Welcome to GCSE Edexcel Maths revision.

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Topic M 23: Percentages and financial maths.

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This video covers Higher tier.

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It includes the shared content and the labelled Higher extensions.

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A percentage means parts per hundred.

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To express A as a percentage of B,

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use the fraction with numerator open bracket A close bracket and denominator open bracket B close bracket ,

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end fraction multiplied by 100 percent,

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with B is not equal to 0 and matching units.

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For percentage change,

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use the fraction with numerator open bracket change close bracket and denominator open bracket original amount close bracket ,

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end fraction multiplied by 100 percent.

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The denominator is the original amount, not the new amount.

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Worked example: A price rises from 40 pounds to 46 pounds.

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Increase equals 6 pounds and percentage increase equals 6 over 40 multiplied by 100 percent equals 15 percent.

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An increase of p percent multiplies by 1 plus the fraction with numerator open bracket p close bracket and denominator open bracket 100 close bracket ,

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end fraction ;

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a decrease multiplies by 1 minus the fraction with numerator open bracket p close bracket and denominator open bracket 100 close bracket ,

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end fraction .

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A 12 percent reduction uses multiplier 0.88.

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Forward and reverse percentage multipliers

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Worked example: 250 pounds reduced by 12 percent becomes 250 multiplied by 0.88 equals 220 pounds.

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Find the new amount directly with the multiplier.

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Reverse a percentage change by dividing by its multiplier.

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A sale price of 72 pounds after a 20 percent reduction came from 72 divided by 0.8 equals 90 pounds.

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A 20 percent rise followed by a 20 percent fall is not no change: 1.2 multiplied by 0.8 equals 0.96, giving an overall 4 percent decrease.

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Simple interest is calculated on the original principal every year.

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At 4 percent simple interest, 500 pounds earns 20 pounds per year, so after 3 years the total is 560 pounds.

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Compound interest applies the percentage to the changing balance.

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Final amount equals P multiplied by open bracket 1 plus the fraction with numerator open bracket r close bracket and denominator open bracket 100 close bracket ,

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end fraction close bracket to the power of open bracket n close bracket for n equal periods at rate r percent per period.

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Worked example: 500 pounds at 4 percent compound interest for 3 years becomes 500 multiplied by 1.04 cubed equals 562 point four three two pounds,

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or 562 pounds and 43 pence to the nearest penny.

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Round the final result, unless the account's rules specify rounding each year.

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Depreciation or decay uses a multiplier below 1.

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A 12,000 pounds car losing 15 percent of its value each year is worth 12,000 multiplied by 0.85 squared equals 8670 pounds after 2 years.

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Rates and periods must match: an annual rate is not applied once per month without converting the model.

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State any assumption that the rate stays constant.

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If money is added or withdrawn each period, a simple power formula may no longer apply.

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Write a recurrence that reflects the order of interest and payments.

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Worked example: A balance earns 2 percent interest, then receives a 100 pounds deposit each year.

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B subscript open bracket n plus 1 close bracket equals 1.02B subscript open bracket n close bracket plus 100.

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Starting at 500 pounds gives 610 pounds after year 1 and 722 pounds and 20 pence after year 2.

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Depositing before interest instead gives B subscript open bracket n plus 1 close bracket equals 1.02 open bracket B subscript open bracket n close bracket plus 100 close bracket ,

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a different result.

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Use the wording to decide the order.

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Find an unknown whole number of periods by repeated calculation or trial powers and check the first period at which the threshold is reached.

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Do not round a time up or down without interpreting the context.

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That completes Percentages and financial maths.

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Revisit the notes and test yourself on the revision website.