Basic / Higher Rate of Tax (Saving Income)

Came across the following example:

Questions:
Taxable Non-Saving Income: $33,950
Taxable Saving Income: $5,550
Total Taxable Income: $39,500

Solution:
Non-Saving Income Tax = $33,950 x 20%
Saving Income Tax = $500 x 0% (Saving Income Nil Rate Band)
= $3,050 ($37,500 – $33950 – $500) x 20%
= $2,000 ($$5,500 – $500 – $3,050) x 40%

My question is why did the author use the higher rate taxpayer of saving income nil rate band ($500), when he use the basic taxpayer rate of 20% in the non-saving income.

How do I justified whether an individual is a basic OR higher rate taxpayer when applying the saving income nil rate band?