# Saving and Borrowing

Before doing this section you should revise the National 4 Lifeskills Maths section on Saving and Borrowing.

There are many savings methods available such as:

• deposit accounts (you can usually withdraw money at any time)
• fixed term savings bonds (these can be from 1 to 5 years but you lose money if you withdraw money early)
• ISA (Individual Savings Account where you pay no tax on your interest)

### Interest

When you save money it earns interest. The account or bond has an interest rate which is applied to the amount of money saved. If money has only been in an account for part of a year, is paid interest only for the time it has been in the account.

Interest is usually compounded, meaning it is added to the amount of savings, to give a new amount for the next interest period.

### Example (Compound interest)

$$\pounds400$$ is deposited in a bank account for 3 years at $$5\%$$ compound interest.

How much money is in the account after the 3 years?

Amount at the start = $$\pounds 400$$

Interest in the 1st year = $$\frac{5}{100}\times400=\pounds 20$$

Amount after 1 year = $$\pounds400\,+\pounds20=\pounds420$$

Interest in the 2nd year = $$\frac{5}{100}\times 420=\pounds21$$

Amount after 2 years = $$\pounds420+\pounds21=\pounds441$$

Interest in the 3rd year =$$\frac{5}{100}\times441=\pounds22.05$$

Amount after 3 years= $$\pounds441+\pounds22.05=\pounds463.05$$

Now try this question:

Question

$$\pounds5000$$ is deposited in a bank account for 3 years at $$4\%$$ compound interest.

How much money is in the account after the 3 years?

Amount at the start = $$\pounds5\,000$$

Interest in the 1st year = $$\frac{4}{100}\times5\,000=\pounds200$$

Amount after 1 year = $$\pounds5\,000+\pounds200=\pounds5200$$

Interest in the 2nd year = $$\frac{4}{100}\times5\,200=\pounds208$$

Amount after 2 years = $$\pounds5\,200\,+\pounds208=\pounds5\,408$$

Interest in the 3rd year = $$\frac{4}{100}\,\times5\,408=\pounds216.32$$

Amount after 3 years = $$\pounds5\,408\,+\pounds216.32=\pounds5\,624.32$$