Before working through this section, make sure that you have worked through the previous section (click here to be taken through to the previous section).

**Example 1**

I place £3,000 into a savings account and receive a compound interest of 5% per year. How much money is in the bank after 4 years?

The interest in this question is compound interest and this means that we will be using the formula that is shown below:

We are told in the question that the amount is £3,000 and the number of years (

*x*) is 4. We are not given the multiplier, but we can work it out from the information given in the question. Interest increases the amount of money, which means that the first step in working out the multiplier is to add the interest rate (5%) onto 100%, which results in the percentage being 105%.The next step is to divide 105% by 100.

The multiplier is 1.05.

We now have everything we need to use the formula; the amount is £3,000, the multiplier is 1.05 and the number of years (

We now have everything we need to use the formula; the amount is £3,000, the multiplier is 1.05 and the number of years (

*x*) is 4.We are working with money, so we need to round our answer to 2 decimal places.

The third decimal place is an 8, which is 5 or above, so we round up. The rounded answer is £3,646.52.

**Example 2**

I borrow £500 at a compound interest rate of 7% per year for 8 years. I pay back the amount of money that I borrow and the interest that is due at the end of the 8 years. How much money do I pay back at the end of 8 years? You may use a calculator.

The process for working out the amount of money that is received when saving and the amount of money owed when borrowing is exactly the same. The only difference is whether the person is getting the money back (saving) or is paying back the bank (borrowing).

- When an individual is saving, they are giving money to the bank and the bank is keeping the money for a period of time (in all of our example, the period of time will be a few years). When the time period is up, the bank will pay the individual the original amount of money and some interest.
- When an individual is borrowing, the bank is giving them money for a period of time. When the period of time is up, the individual must pay the initial amount that has been borrowed plus an amount of interest back to the bank.

We are going to work out the amount of money that the individual owes the bank by using the generic formula, which is given below.

*x*in the above formula is the number of years, which is 8. The amount borrowed is £500. We can work out the multiplier by adding the amount of interest to 100% and dividing by 100. The interest that is paid on the amount borrowed is 7%, which when added to 100% is 107%.We then need to divide by 100, which means that the multiplier value is 1.07.

We are now able to sub the appropriate values into their respective places in the formula. The amount borrowed is £500, the multiplier is 1.07 and the number of years (

*x*) is 8.As this is money, it needs to be rounded to 2 decimal places

Therefore, after 8 years of borrowing £500 at an interest rate of 7%, the individual will owe the bank £859.09.

**Example 3**

We are now going to have a look at a question whereby we are just asked to find the amount of interest that is earnt. We answer questions like this by using the formula to work out the total amount of money in the bank account (the same process as the previous questions). We then find the interest by taking the amount of money in the account at the start away from the amount of money at the end. Let’s have an example.

I place £1,360 into a bank account for 9 years. The money receives a compound interest of 2.1% per year. How much interest do I earn?

The first step in answering this question is to work out the total amount of money in the bank account after the 9 years. We can do this by using the compound interest formula below:

We are told that the amount of money saved is £1,360 and the number of years (

*x*) is 9. We do not have the multiplier value, but we can work it out from the information given in the question. The first step in finding the multiplier is to add the interest rate (2.1%) onto 100%, which gives us 102.1%.We now divide by 100.

The multiplier is 1.021.

We now have everything we need for the formula; the amount of money is £1,360, the multiplier is 1.021 and the number of years is 9. We sub these values into the formula.

We now have everything we need for the formula; the amount of money is £1,360, the multiplier is 1.021 and the number of years is 9. We sub these values into the formula.

We are working with money, which means that we need to round our answer to 2 decimal places.

The third decimal places is a 3, which means that we round down because 3 is less than 5. Therefore, the amount of money in the account at the end of the 9 years is £1,639.72.

The question asks us to work out the amount of interest earnt. We can find this out by taking the original amount of money (£1,360) away from the final amount in the bank account (£1,639.72).

The question asks us to work out the amount of interest earnt. We can find this out by taking the original amount of money (£1,360) away from the final amount in the bank account (£1,639.72).

The amount of interest earnt is £279.72.

**Example 4 – A Depreciating Asset**

Depreciating means to fall in value. An example of a depreciating asset is a phone, which will decrease in value over time. Phones decrease in value because technology moves on and the battery life of the phone becomes worse. Another example of a depreciating asset is a car and a car is going to be our example.

I purchase a car for £25,000. The car decreases in value by 8% per year. How much will the car be worth in 4 years time? You may use a calculator.

We are going to be using the generic formula, but with a few modifications.

*x*in our formula is the number of years and in this example, we are looking at the value of the car after 4 years, so

*x*is 4. The initial value of the car is £25,000. Finally, we need to work out the multiplier. The value of the car is decreasing, and this means that we need to take the percentage decrease in the value of the car off of 100%.

This gives us a percentage value of 92% (100%-8%). The next step is to divide our answer by 100, which gives us the multiplier as 0.92 (a multiplier with a value less than 1 will decrease our answer). We are now ready to use the formula.

This gives us a percentage value of 92% (100%-8%). The next step is to divide our answer by 100.

The multiplier is 0.92 (a multiplier with a value less than 1 will decrease our answer).

We are now ready to use the formula; the initial value of the car is £25,000, the multiplier is 0.92 and the number if years (

We are now ready to use the formula; the initial value of the car is £25,000, the multiplier is 0.92 and the number if years (

*x*) is 4.As this is money, it needs to be rounded to 2 decimal places

After 4 years, the car is worth £17,909.82.

There are quite a few more questions in the quiz so have a go at answering those.

There are quite a few more questions in the quiz so have a go at answering those.