From 6 April 2016, basic rate taxpayers can earn up to £1,000 in savings income tax-free. Higher rate taxpayers can earn up to £500. These are called the Personal Savings Allowance.
Savings income includes account interest from:
- bank and building society accounts
- accounts with providers like credit unions or National Savings and Investments
- interest distributions (but not dividend distributions) from authorised unit trusts, open-ended investment companies and investment trusts
- income from government or company bonds
- most types of purchased life annuity payments.
You can see examples at ACCA's UK technical advice and support pages. 
In the following examples the following limits are assumed:
Personal allowance                                      £11,000
Basic rate limit                                              £32,000
Higher rate threshold                                    £43,000
 
Example 1
Mr X has salary income of £20,000 and received £1,500 interest for the year.
Salary                                                            20,000
Interest received                                              1,500
                                                                       21,500
Personal allowance                                       (11,000)
                                                                        10,500
Personal savings allowance                            (1,000)
Income taxed at 20%                                        9,500
Tax payable £9,500 x 20% = £1,900