The multiplier method

Compound interest problems are much easier to solve by using the multiplier method.

For example, a 5% increase on the original balance in a bank would mean there is now 105% in the bank. This is the same as 1.05 as a decimal so this is the multiplier.

Examples

Calculate the interest on borrowing £40 for 3 years if the compound interest rate is 5% per year.

  • Year 1: \pounds 40 \times 1.05 = \pounds 42
  • Year 2: \pounds 42 \times 1.05 = \pounds 44.10
  • Year 3: \pounds 44.10 \times 1.05 = \pounds 46.31

This calculation can be made more concise by using powers.

To calculate the money in the bank after 3 years the calculation would be:

40 \times 1.05 \times 1.05 \times 1.05 = 46.31

This can also be written as:

40 \times 1.05^3 = 46.31

Using powers saves a lot of steps if the time period for the calculation is large.

Question

£500 is invested in a bank account that receives 3% compound interest per year. How much will be in the bank account after 7 years?

500 \times 1.03^7 = \pounds 614.94

Question

A car depreciates in value by 8% per year. It was bought for £10,000. How much is it worth after 5 years?

10,000 \times 0.92^5 = \pounds 6,590.82

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