Percentages

Percentages

1. Percentage of amounts

   • Percentages of amounts can be calculated by writing the percentage as a fraction or decimal and then multiplying it by the amount in question.
   • Example
     • Find 20% of 70
       • (20/100) x 70
       • 70 x 0.2
       • 20% x 70

2. Percentage increase and decrease

   • To increase or decrease an amount by a percentage, first calculate the percentage of the amount and then either add this answer on to increase the quantity, or subtract this answer to decrease the quantity. There is more than one way to find the percentage of an amount.
   • Example
     • Increase
       • Increase £50 by 8%
         • Using the multiplying method, first find 8% of £50: Equation: (8/100) x 50 = 4 8% of £50 is £4, so to increase £50 by 8%, add the £4 onto the £50, which is £54.
         • 50 x 1.08
     • Decrease
       • Do the same method but rather than add on, minus from the original
       • 50 x 0.92

3. Percentage change

   • Percentage change is calculated by dividing the difference between the two amounts by the original amount.
   • Example
     • A brooch is bought at a car boot sale for £40. It is later sold in a shop for £50. What is the percentage profit?
       • 10/40 x 100
   • Difference/original x 100

4. Repeated percentage change

   • Example
     • An original value of 378 is increased by 89% every year for 2 years. What is the new value?
       • 378 × 1.89squared = 1350.2538
   • Can be calculated by x the original number with percentage increase and then squaring,cubing,etc....by however many years or months

5. Interest

   • Simple interest
     • Simple interest is worked out by calculating the percentage amount and multiplying it by the number of periods that the money will be invested for
       • Example
         • Calculate the interest on borrowing £40 for 3 years if the simple interest rate is 5% per year
           • First, work out the amount of interest for 1 year by working out 5% of £40, which is £2
             • The money is being loaned for 3 years, so multiply this amount by 3: 3 x 2 = £6
   • Compound interest
     • compound interest changes the amount of money in the bank each time and a new calculation has to be worked out.
       • Calculate the interest on borrowing £40 for 3 years if the compound interest rate is 5% per year.
         • 40 x 1.05cubed
           • £46.30