Tax – Calculating Percentages on Goods and Income
Tax is a compulsory payment collected by governments on goods, services, income, and transactions. Understanding how tax is calculated as a percentage is essential for everyday life — from shopping to payslips.
Types of Tax
| Tax Type | What It Applies To | Typical Rate (UK example) |
|---|---|---|
| VAT (Value Added Tax) | Most goods and services | 20% standard rate |
| Income Tax | Earnings above a threshold | Various bands (20%, 40%, 45%) |
| Council Tax | Residential properties | Varies by local authority |
| Stamp Duty | Property purchases | Varies by price band |
Calculating Tax on a Purchase
Tax Amount = Tax Rate% times Original Price / 100. Total Price = Original Price plus Tax Amount. Or: Total = Original times (1 + Tax%/100).
Worked Examples
VAT at 20% on a 350 item.
VAT = 20% of 350 = 70. Total price = 350 + 70 = 420. Or: 350 times 1.20 = 420.
A price tag shows 480 including 20% VAT. Find the pre-tax price.
480 = pre-tax price times 1.20. Pre-tax = 480 / 1.20 = 400.
A salary of 30,000. The first 12,570 is tax-free. 20% tax on the rest.
Taxable income = 30,000 - 12,570 = 17,430. Tax = 20% of 17,430 = 3,486. Take-home = 30,000 - 3,486 = 26,514.
Tax-Inclusive vs Tax-Exclusive Prices
| Scenario | Calculation |
|---|---|
| Add tax to a price | Price times (1 + rate/100) |
| Find pre-tax from inclusive price | Inclusive price divided by (1 + rate/100) |
| Find how much tax was paid | Inclusive price minus pre-tax price |
Key Takeaways
- Tax is calculated as a percentage of the taxable amount.
- Total price (tax-inclusive) = pre-tax price times (1 + tax rate/100).
- To find the pre-tax price: divide the inclusive price by (1 + tax rate/100).
- Always check whether a quoted price includes or excludes tax.
Practice Questions
- Calculate VAT at 20% on a 75 purchase. What is the total?
- A price is quoted as 960 including 20% VAT. What is the pre-VAT price?
- A person earns 45,000 per year. The first 12,570 is tax-free; the next 37,700 is taxed at 20%. How much income tax do they pay?
- A restaurant adds a 12.5% service charge to a 64 bill. What is the total?
- How much VAT is included in a 180 tax-inclusive price, if the VAT rate is 20%?