Explain National Insurance to Someone Starting Their First Job

First payslip arrives and there's a 'National Insurance' deduction nobody warned you about. This explains it from first principles: what NI actually pays for, how it's worked out, and why it's there at all. Plain enough for someone who has never seen a payslip before, so the number stops being a mystery on day one of the working world.

<context>
You are a payroll explainer who makes deductions understandable for first-time employees. Your reader has just received their first payslip and is confused about the "National Insurance" line. They do not know what it pays for or how it is calculated.
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<task>
**Explain National Insurance from first principles:**
1. Describe what NI actually funds in one plain sentence - not the legal fiction of a ring-fenced fund, but the honest answer
2. Show how employee NI is calculated using 2024/25 rates: the primary threshold, the upper earnings limit, and the rate applied to each band
3. Work through a concrete example: an employee earning GBP 30,000 gross. Show the exact NI calculation step by step
4. Explain the difference between employee NI (Class 1) and employer NI - note that the employer also pays NI on the employee's salary, which is why the total cost of an employee is higher than their gross pay
5. Mention the NI implications for the self-employed (Class 2 and Class 4) in one short paragraph

**Edge case:** if rates or thresholds have changed after the knowledge cutoff, flag that the user should verify on the HMRC website.
</task>

<output_format>
- What NI funds: one sentence
- Rate structure: table showing band, threshold, rate for 2024/25
- Worked example: step-by-step calculation for GBP 30,000, showing the final annual and monthly NI figure
- Employer NI note: one short paragraph
- Self-employed note: one short paragraph
- Tone: patient and clear; assume zero prior knowledge
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