## What is interest?** **

This guide is about compound interest, but before we get to that it’s important to understand what interest actually is. Well, interest is usually paid when money has been lent or borrowed. It is basically money paid at a specific percentage and at regular intervals. The best example of interest in real life is with banks. Banks will charge their customers interest on money they borrow and reward customers with interest on money they deposit with the bank.

## What is compound interest?

Compound interest essentially means that interest is paid on the amount saved/ owed and the previous interest payments. With compound interest the amount of money saved/owed changes each time an interest payment is added, so a new calculation is made which includes the previous interest added.

This all becomes much easier to understand when we look at an example.

#### Example 1

Let’s imagine we deposit £200 in a bank account paying 5% compound interest per year. This is how compound interest would work over three years (if we didn’t make any withdrawals or deposits):

First Year: £200 + 5% = £200 + £10 = £210

Second Year: £210 + 5% = £210 + £10.50 = £220.50

Third Year: £220.50 + 5% = £220.50 + 11.03 = £231.53

Notice how the amount used to calculate the interest paid changes each year to include the interest added in previous years. That’s compound interest.

### The multiplier method for compound interest

At this point you might be thinking, “this compound interest thing is all well and good, but won’t it take ages to work out the interest added over multiple years?”

Well, yes it would if we had to do individual calculations for each year. There is a much faster method though, which will allow you to ‘jump’ ahead by multiple years at a time. You need to use the multiplier method for percentage increases and put that multiplier to the power of the number of years (or time periods) you need to work out. For more help with the multiplier method for percentage increases, check out our guide here.

Let’s use the multiplier method for the example we looked at above. With £200 saved in an account paying 5% compound interest over 3 years our calculation should look like this:

That makes the calculation so much easier and saves you a lot of time. Let’s try one more example.

Example 2

Lara invests £1500 in a bank account paying 2% compound interest. She leaves her money in the account for 7 years, without making any withdrawals. How much money will Lara have in the account after 7 years?

To answer this one take the amount of money Lara started with and multiply it by the decimal multiplier to increase by 2%, which is 1.02. Put the 1.02 to the power of 7 (for the number of years we’re looking at in this question). Then let your calculator do the hard work:

## Depreciation

Depreciation is essentially a compound measure in the opposite direction, so decreasing the original value at a specific percentage at regular intervals. For depreciation you need to use the multiplier method for decreasing percentages and put this multiplier to the power of the number of time intervals in the question.

#### Example 1

Ben purchased a car for £9000. His new car will depreciate by 12% each year. How much will his car be worth after 4 years?

Start by working out the decimal multiplier to decreased by 12%. 100% – 12% = 88%, so the multiplier is 0.88.

Take the original value of the car, multiply it by 0.88 to the power of 4 (for the number of years in the question).

### Practice Questions

Have a go at the practice questions below on compound interest and depreciation. You can contact us directly if you’d like any specific help from one of our tutors.

- Lola saved £2100 in a bank account paying 3% compound interest. Assuming she makes no withdrawals, how much money will she have after 6 years?
- Steven buys a new plant. The plant grows at a compound rate of 8% every week. On the first day the plant is 9cm tall. How tall will the plant be after 5 weeks?
- The population of a small town was 5600 in 2016. The population is expected to increase at a rate of 2.5% per year. How many people would you expect to live in the town in 2026?
- Sheila buys a car for £12,500. She expects the car’s value to depreciate by 15% each year. How much should Sheila expect her can to be worth after 2 years?
- Fred has £1400 in his savings account. He is not expecting to deposit any more money in the account, but he will be spending 18% of the money in his account each month. How much money will he have left after 2 year ?

Check your answers below.

Answers:

- £2507.51
- 13.22cm
- 7168
- £9031.25
- £11.96