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Compound interest is paid or earned not only on the original amount but also on the interest added each year.

Example

A builder borrows £5000 from her bank. It will be paid back after 3 years with compound interest added at 4% per annum.

How much will she have to pay back after 3 years?

Solution

• At the end of Year 1, she will owe £5000 + 4% of £5000.
  5000 + 5000 x 0.04 = £5200
• At the end of Year 2, she will owe £5200 + 4% of £5200. 5200 + 5200 x 0.04 = £5408
• At the end of Year 3, she will owe £5408 + 4% of £5408. 5408 + 5408 x 0.04 = £5624.32

Answer:

The builder will owe £5624 after 3 years.

Alternative method

For the end of Year 1, instead of multiplying £5000 by 0.04 and adding £5000, we could multiply £5000 by 1.04.
We could do this for the next two years also.

Therefore, a much quicker calculation is:
5000 x 1.04 x1.04 x 1.04 or
5000 x 1.04³ = £5624.32

Answer:

The builder will owe £5624 after 3 years.

Example

Jessica invests £35000 for 4 years at 6% compound interest.
How much will her investment be worth after this time?

Solution

The compound interest is 6%, so we need to multiply by 1.06 each year.
There are 4 years to calculate, so the calculation is:

35000 x 1.06⁴ = 44186.6936

Answer:

Jessica’s investment is worth £44186.69 (to the nearest penny).

Tax is money collected by the government to provide public services.
The most common taxes are income tax and value-added tax (VAT).

Income tax is money deducted from salary or wages. The amount you pay will depend on how much you earn. Typically, the first portion of income isn’t taxed. This is called your personal allowance.

The rest of your salary above your personal allowance is called taxable income. This is the money your income tax is calculated on.

VAT is a tax which has to be paid when you buy items in a shop, restaurant or online. It is also added for some services such as building work or car repairs.

Example

The table below shows the income tax rate which is applied to different annual incomes in the UK.

How much income tax do the following people pay per year?

Anna who earns £12000 per annum.

Solution:

Anna earns less than £12570, so her tax rate is 0%.

She does not have to pay any income tax.

Answer:
Anna pays zero income tax.

Mark who earns £25000 per annum.

Solution:

Mark will have to pay income tax at a rate of 20% but will not have to pay any on the first £12570.

His taxable income is £25000 - £12570 = £12430 20% of 12430 = 12430 x 0.2 = £2486

Answer:

Mark pays £2486 in income tax.