In aptitude (Compound Interest), A invests ₹x in a bank for 2 years. The bank gives 5% interest in year 1 and 6% interest in year 2, compounded annually. If the amount received after 2 years is ₹24,486, what is the value of x (in ₹)?

Introduction / Context:
This question involves compound interest with different rates applied in each year. Instead of a single flat rate, the first year grows at 5% and the second year at 6%. You are required to work backwards from the final amount to find the initial principal. This situation models real bank products where promotional rates or changing economic conditions affect annual returns.

Given Data / Assumptions:

• Initial principal invested = ₹x (unknown).
• Year 1 interest rate = 5% per annum.
• Year 2 interest rate = 6% per annum.
• Interest is compounded annually.
• Final amount after 2 years = ₹24,486.
• We need to determine x, the original investment.

Concept / Approach:
For compound interest with varying rates, each year multiplies the previous year amount by a factor of 1 plus the rate. Thus: Amount after Year 1 = x * (1 + 5 / 100) = x * 1.05. Amount after Year 2 = Amount after Year 1 * (1 + 6 / 100) = x * 1.05 * 1.06. This final amount is given as ₹24,486. So we have: x * 1.05 * 1.06 = 24,486. To find x, divide the final amount by the product 1.05 * 1.06.

Step-by-Step Solution:
Step 1: Express the final amount: Final amount = x * 1.05 * 1.06. Step 2: Set this equal to 24,486: x * 1.05 * 1.06 = 24,486. Step 3: Compute the combined growth factor: 1.05 * 1.06 = 1.113. Step 4: Rearrange to get x = 24,486 / 1.113. Step 5: Perform the division: 24,486 divided by 1.113 equals 22,000. Step 6: Therefore, the initial principal x is ₹22,000.

Verification / Alternative check:
Verify by forward calculation using x = ₹22,000. After year 1: Amount after Year 1 = 22,000 * 1.05 = 23,100. After year 2 at 6%: Amount after Year 2 = 23,100 * 1.06 = 24,486. This matches the given final amount perfectly, confirming that ₹22,000 is correct.

Why Other Options Are Wrong:
₹21,500, ₹22,500, ₹23,000, and ₹24,000 all yield different final amounts when multiplied by factors 1.05 and 1.06; none of them produce exactly ₹24,486. Only ₹22,000 leads to the correct final amount, so it is the only valid choice.

Common Pitfalls:
Students sometimes incorrectly add the rates to get 11% and then apply that single rate for 2 years, treating the problem like simple interest. Others forget that multiplication order matters and may round intermediate values too early. Always use the multiplicative factors year by year and postpone rounding until the end to keep accuracy high.

Final Answer:
The principal amount invested so that it grows to ₹24,486 under 5% in the first year and 6% in the second year, compounded annually, is ₹22,000.