If the rate of inflation for the next 20 years is expected to be 2.5% per year, what annual income will be needed 20 years from now to have the same purchasing power as a Rs. 30,000 annual income today?

Introduction / Context:
This question illustrates the effect of inflation on purchasing power. Even if your nominal income stays the same, rising prices mean that you can buy less in the future with the same rupee amount. To maintain today's standard of living, you need to adjust your future income upward using the inflation rate.

Given Data / Assumptions:

• Current annual income with desired purchasing power = Rs. 30,000
• Annual inflation rate = 2.5% per year
• Time horizon T = 20 years
• Prices grow at a steady rate of 2.5% every year
• We want the future nominal income that has the same purchasing power as Rs. 30,000 today

Concept / Approach:
The future cost of the same basket of goods is increased by inflation. If prices rise at rate i per year, then after T years, the price level multiplies by (1 + i)^T. Therefore, the required future income F to match a present income P in real terms is:
F = P * (1 + i)^THere P = 30000 and i = 2.5% = 0.025.

Step-by-Step Solution:
Step 1: Identify the formula.F = 30000 * (1.025)^20Step 2: Compute (1.025)^20 approximately.(1.025)^10 ≈ 1.28 (approximate)Then ((1.025)^10)^2 ≈ 1.28^2 ≈ 1.6384More accurately, (1.025)^20 ≈ 1.6386Step 3: Multiply by the present income.F ≈ 30000 * 1.6386 ≈ 49,158

Verification / Alternative check:
If we instead used a financial calculator or spreadsheet with P = -30000, rate = 0.025, nper = 20, we would again obtain a future value around 49158. This confirms that about Rs. 49,158 is required in 20 years to buy what Rs. 30,000 buys today, assuming 2.5% inflation each year.

Why Other Options Are Wrong:
Rs. 39,158: This would correspond to a lower effective inflation rate than 2.5%.Rs. 59,158 and Rs. 69,158: These correspond to higher inflation assumptions or a longer time horizon.Rs. 45,000: A rough guess that does not match the compound inflation calculation.

Common Pitfalls:
A frequent mistake is to treat inflation linearly and multiply 2.5% by 20 to get 50% total, then calculate 30000 * 1.5 = 45000. This ignores compounding of inflation. In reality, inflation itself compounds, so the total increase is more than 50%. Using (1 + i)^T is essential for accurate long-term financial planning.

Final Answer:
An annual income of approximately Rs. 49,158 will be needed 20 years from now to match the purchasing power of Rs. 30,000 today at 2.5% annual inflation.