Question 9.24 Choose the correct answerMs. Moneypenny’s wealth depreciates at £5,000 a year. Her net annual income is £25,000. She will spend 40% of this net income on an extension on the house, another 40% on general consumption and save the remaining 20% in a pension fund. The tax rate is 40%. Based on this information, which of the following statements is correct?

Question

BlackTom AI · Accepted Answer

Her savings (investment) equals 20% of her net income: 0.20 × £25,000 = £5,000.

1) Relevant concepts
- Net (after‑tax) income is the amount available for consumption, saving and investment after taxes.
- Percent allocations of net income are computed by multiplying the net income by the given percentages.
- Depreciation reduces the stock of wealth; gross saving/investment minus depreciation gives the change in wealth.

2) Step‑by‑step reasoning and intermediate calculations
- Net annual income = £25,000.
- Amount spent on house extension = 40% of £25,000 = 0.40 × £25,000 = £10,000.
- Amount on general consumption = 40% of £25,000 = £10,000.
- Amount saved in pension (investment) = 20% of £25,000 = 0.20 × £25,000 = £5,000.
- Wealth depreciates by £5,000 per year. Net change in wealth = investment − depreciation = £5,000 − £5,000 = £0 (so saving just offsets depreciation).

3) Why the correct answer is correct
- Option (a) states “Her investment is £5,000.” The pension saving is explicitly 20% of net income; the calculation above yields £5,000, so (a) is correct.

4) Why the other options are incorrect
- (b) “Her before‑tax income is £50,000.” If tax rate is 40% and net income is £25,000, gross income G satisfies 0.6G = £25,000 → G = £25,000/0.6 = £41,666.67, not £50,000.
- (c) “She pays a tax of £12,000.” Using G = £41,666.67, tax = 0.40 × G = £16,666.67, not £12,000.
- (d) “Her annual disposable income is £20,000.” Disposable income (after tax) is given as net annual income = £25,000, so £20,000 is incorrect.

Conclusion: The correct statement is (a) Her investment is £5,000, which matches the provided answer.

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