Equity represents the owners' stake in a business. It's the residual interest in the assets of the business after deducting all liabilities. Essentially, it's what would be left for the owners if all the assets were sold and all the debts were paid.

Liabilities, on the other hand, are what the business owes to external parties (creditors) – such as loans, salaries payable, and accounts payable. Equity is the difference between the business's assets and its liabilities. A simple way to think about it is: Equity = Assets - Liabilities. If liabilities exceed assets, the business is insolvent.

Issued Share Capital: This is the total value of shares that a company has offered to the public for sale. In this case, ABC Ltd issued 1000 shares. The total issued capital is therefore 1000 shares x £1/share = £1000.

Called-Up Share Capital: This is the portion of the issued share capital that the company has asked the shareholders to pay. Here, £0.50 per share has been called up, meaning 1000 shares x £0.50/share = £500 has been called up.

Paid-Up Share Capital: This is the amount that shareholders have actually paid to the company in exchange for their shares. Since all called-up shares have been fully paid, the paid-up share capital is equal to the called-up share capital. Therefore, the paid-up share capital is £500.

In this scenario:

• Issued Share Capital: £1000
• Called-Up Share Capital: £500
• Paid-Up Share Capital: £500

The key difference between a sole trader and a limited company lies in the liability of the owner. A sole trader and a limited company have very different legal structures regarding personal responsibility for business debts.

Here's a table summarizing the differences:

In essence, a sole trader is personally liable for all business debts, while a limited company separates the business from the owner, limiting the owner's liability to the amount invested in the company.