Albert invests ₹x in a fixed deposit account. The bank applies 10% interest for the first year and 15% interest for the second year, compounded annually. If the final amount after 2 years is ₹20,240, what is the value of x (in ₹)?

Introduction / Context:
This problem is about compound interest with different interest rates in each year. Instead of a single constant rate, the bank offers 10% in the first year and 15% in the second year. The question asks you to reverse the compounding process to find the original investment. Such questions strengthen your understanding of how compound growth works when the rate changes over time, which is very relevant to real world financial products.

Given Data / Assumptions:

• Initial principal = ₹x (unknown).
• Year 1 interest rate = 10% per annum.
• Year 2 interest rate = 15% per annum.
• Interest is compounded annually.
• Final amount after 2 years = ₹20,240.
• We need to find x, the original principal.

Concept / Approach:
Under compound interest with variable rates, each year multiplies the amount by a factor 1 + r/100 corresponding to that year. Therefore: Amount after Year 1 = x * (1 + 10 / 100) = x * 1.10 Amount after Year 2 = Amount after Year 1 * (1 + 15 / 100) = x * 1.10 * 1.15 The final amount after 2 years is given as ₹20,240, so we set: x * 1.10 * 1.15 = 20,240 Then we solve for x by dividing the final amount by the combined growth factor 1.10 * 1.15.

Step-by-Step Solution:
Step 1: Write the compound growth expression: Final amount = x * 1.10 * 1.15. Step 2: Given final amount = 20,240, so x * 1.10 * 1.15 = 20,240. Step 3: Compute the combined growth factor: 1.10 * 1.15 = 1.265. Step 4: Rearrange for x: x = 20,240 / 1.265. Step 5: Perform the division: 20,240 divided by 1.265 equals 16,000. Step 6: Therefore, the original principal x is ₹16,000.

Verification / Alternative check:
Verify by forward computation. Starting from x = ₹16,000: Amount after Year 1 = 16,000 * 1.10 = 17,600. Amount after Year 2 = 17,600 * 1.15 = 20,240. This final amount exactly matches the value given in the question, so the principal is confirmed as ₹16,000.

Why Other Options Are Wrong:
₹14,000: Compounding 14,000 with 10% and then 15% yields a final amount less than 20,240.
₹15,000: This also grows to a value lower than 20,240 under the same sequence of rates.
₹18,000 and ₹17,000: Both would produce final amounts greater than 20,240 when compounded at 10% and then 15%, so they do not satisfy the given condition.

Common Pitfalls:
A common error is to wrongly treat the problem as simple interest by adding 10% and 15% and using a combined 25% on the principal. That approach ignores the compounding effect and leads to the wrong answer. Another pitfall is to add interest amounts year by year in rupees without using the multiplicative factors. Always express each year as multiplication by 1 plus the rate, then multiply the factors and solve backward when the final amount is known.

Final Answer:
The original investment amount that grows to ₹20,240 under 10% interest in the first year and 15% interest in the second year is ₹16,000.