Compound interest is when the interest earnt during one period is added to the amount saved (or borrowed). This amount of interest is then able to earn interest in any subsequent period. Essentially the interest that is earnt in each period is added to the amount saved, which means that one will earn more interest in the next period.

There are two different ways to work out compound interest; one way is to work out the interest in each period and then add it to the amount that was saved. This will then be the new amount of money that will earn interest for the next year. We would then keep doing this until we reach the amount of years that the money has been saved for. The second method is to use one calculation that we plug into the calculator to find out the final value amount.

We calculate compound interest for both savings (keeping money in a bank) and borrowing (taking money from a bank). When an individual saves they receive the amount of money that they saved back and some interest, which is the reward for saving. When an individual borrows, they must pay the amount of money that they borrowed back and some interest, which is the cost of borrowing the money. We will look at examples that are about borrowing and saving.

There are two different ways to work out compound interest; one way is to work out the interest in each period and then add it to the amount that was saved. This will then be the new amount of money that will earn interest for the next year. We would then keep doing this until we reach the amount of years that the money has been saved for. The second method is to use one calculation that we plug into the calculator to find out the final value amount.

We calculate compound interest for both savings (keeping money in a bank) and borrowing (taking money from a bank). When an individual saves they receive the amount of money that they saved back and some interest, which is the reward for saving. When an individual borrows, they must pay the amount of money that they borrowed back and some interest, which is the cost of borrowing the money. We will look at examples that are about borrowing and saving.

**Example 1**

I save £80 and receive a compound interest rate of 10%. How much money do I have after 3 years?

We are going to be looking at answering this question using two different methods. Usually you would answer compound interest questions by using the multiplier method, which is the second method. The first method is there to help you understand compound interest. If you are ok with compound interest, feel free to skip the first method.

**Method 1: Each Year**

With compound interest, the interest that is earnt during each period is added to the amount of money at the start of the period. Let’s start by working out the amount of money at the end of year 1. The amount of money at the end of year 1 will be.

We now need to work out how much interest is earnt during the first year. We are able to work out what 10% of £80 is by dividing by 10.

This tells us that £8 interest was earnt during the first year. The next step is to add this amount of interest to the original amount.

After year 1, the amount of money in this individual’s bank account is £88. This is the amount of money that will earn interest during year 2. We can work out the amount of money that our individual has at the end of year 2 by using a similar formula to the one above.

The amount of money at the end of year 1 is £88 and the interest earnt in year 2 is 10% of the total amount of money that is in the bank account in year 2. 10% of £88 is £8.80 (to obtain 10%, I divided the amount saved (£88) by 10). We are now able to sub the values into the above formula.

Therefore, after the second year, I have £96.80 in my bank account.

We now need to work out the amount of money after year 3 and again we used a similar formula to before.

We now need to work out the amount of money after year 3 and again we used a similar formula to before.

The interest earnt in year 3 is 10% of £96.80, which is £9.68

Therefore, the amount of money that our individual has in their bank account after 3 years is £106.60 and the amount of interest that he earnt was £26.48 (£106.48 - £80).

**Method 2: Multiplier**

We are now going to use the multiplier method to find the amount of money that our individual has after 3 years. The multiplier method has the following formula:

*x*in the above formula is the number of years that the money is saved for, which in our example is 3. We looked at the multiplier in a previous section (click here to be taken through to that section). Interest is being added to the amount of money that is in the bank account, which means that we obtain the multiplier by adding the amount of interest to 100% and then dividing by 100. Therefore, we add 10% to 100%, which gives us 110%.

We now divide by 100, which gives us a value for the multiplier of 1.1.

The next step is to sub the amount (£80), the value for the multiplier (1.1) and the number of years (

*x*as 3) into the formula above.We are now able to work out the amount of interest earnt over the 3 years, which is £26.48 (£106.48 - £80). This is exactly the same as we found by using the other method. The multiplier method is considerable faster at obtaining the answer.

**Same Question, but with Simple Interest**

I am now going to have a look at answering the question where simple interest is used rather than compound interest. The question would be:

I save £80 and receive simple interest of 10% per year. How much money do I have after 3 years?

With simple interest, the amount of interest earnt per year is the same amount throughout all of the years; the amount of interest earnt per year is the same for year 1, year 2 and year 3.

The interest rate is 10% per year. We can find 10% of £80 in two ways; we could use the method that I used earlier, or we could use the multiplier method. The multiplier method involves turning 10% into a multiplier (decimal) and then multiplying the multiplier by the amount saved. 10% as a multiplier is 0.1 (10 ÷ 100 = 0.1). Therefore, we multiply the multiplier (0.1) by the amount saved (£80).

We are working out simple interest, so the interest earnt in each of the 3 years will be £8 and this means that the total amount of interest earnt is £24 (£8 x 3 = £24). To find the amount of money that our individual has in his savings account after 3 years, we need to add the interest earnt to the original amount that was in the savings account.

You can see that the amount of money at the end of 3 years when we are using simple interest (£104) is less than the amount of money when we are using compound interest (£106.48). This will always be the case when the interest rate is the same.