Not all percentages can be expressed as simple fractions and often figures such as 4.26% may need to be used. In these cases it is often better to work with decimals.
Worked Examples
The cost of a car is £20 000. VAT at 16.5% has to be added to this bill. Find the VAT and the total bill.
Use 16.5% = 0.165.
Then
| 16.5% of £20 000 | = 0.165 × £20 000 |
| = £3300 |
So the total bill is
£20 000 + £3300 = £23 300
Jamie has £486.27 in his building society account which earns interest of 8.21% per year. How much interest does he get and how much money does he have in his account after the first year?
Writing 8.21% as a decimal gives 0.0821.
| 8.21% of £486.27 | = 0.0821 × £486.27 |
| = £39.92 (to the nearest p) |
So at then end of the first year Jamie has
£486.27 + £39.92 = £526.19
in his account.
The cost of building materials for a garage and storeroom is £28 800 plus VAT at 16.5%. Find the total cost of the building materials.
100% represents the original cost (£28 800).
16.5% is the increase due to VAT.
100% + 16.5% = 116.5%
So the total cost can be found in one stage by finding 116.5% of £28 800.
Note that 116.5% is 1.165 as a decimal.
So
| 116.5% of £28 800 | = 1.165% × £28 800 |
| = £33 552 |
The total cost of the load of blocks is £33 552.
Jessica's salary of £48 000 is to be increased by 2.5%. Find her new salary.
Her new salary is 102.5% of her old salary.
| 102.5% of £48 000 | = 1.025 × £48 000 |
| = £49 200 |
Her new salary is £49 200.
A holiday cruise to New York for a family costs £9995, but a special offer gives an 8.5% discount. Find the price of the cruise with the discount.
With an 8.5% discount, 91.5% of the original price must be paid.
(100% − 8.5% = 91.5%)
So
| 91.5% of £9995 | = 0.915 × £9995 |
| = £9145.43 (to the nearest p) |
The discounted price is £9145.43.
Janet's gross salary is £2400 per month. Her tax-free allowances are shown below.
National Insurance 5% of gross salaryCalculate
her gross yearly salary
Show me| Janet's gross yearly salary | = £2400 × 12 |
| = £28 800 |
her total tax-free allowances for the year
Show me| National Insurance | = × £28 800 per year |
| = £1440 per year |
| Personal Allowance | = £3000 per year |
| Total tax-free allowances for the year | = £1440 + £3000 |
| = £4440 |
her taxable yearly income.
Show me| Taxable yearly income | = £28 800 − £4440 |
| = £24 360 |
A 10% tax is charged on the first £20 000 of taxable income. A 20% tax is charged
on the portion of taxable income above £20 000.
Calculate the amount of income tax Janet pays.
| Tax on first £20 000 of taxable income | = × £20 000 |
| = £2000 |
| Tax on remaining £4360 of taxable income | = × £4360 |
| = £872 |
| Total tax paid | = £2000 + £872 |
| = £2872 per year |
Exercises
