At a compound interest rate of 10% per annum, the amount received after 3 years is Rs 10,648. For this 3 year period, what was the original principal amount invested (in rupees)?

Introduction:
This compound interest question asks you to find the original principal when you know the final amount, rate of interest, and time. Such reverse calculations are very common in banking exams and finance related aptitude tests, and they test your comfort with rearranging the compound interest formula.

Given Data / Assumptions:

• Final amount A after 3 years = Rs 10,648
• Annual interest rate r = 10% per annum
• Time t = 3 years
• Compounding is annual
• We need to find the principal P

Concept / Approach:
The compound interest amount for annual compounding is given by:
A = P * (1 + r)^twhere r is expressed as a decimal. To find P, we rearrange the formula as:
P = A / (1 + r)^tThis direct substitution approach avoids unnecessary steps and gives an exact value of principal.

Step-by-Step Solution:
Step 1: Convert the rate to decimal.r = 10% = 10 / 100 = 0.10Step 2: Write the amount formula.A = P * (1 + 0.10)^3A = P * (1.10)^3(1.10)^3 = 1.10 * 1.10 * 1.10 = 1.331So 10,648 = P * 1.331Step 3: Solve for P.P = 10,648 / 1.331P = Rs 8,000So the principal amount invested must have been Rs 8,000.

Verification / Alternative check:
We can verify the result by forward calculation. With P = Rs 8,000 and r = 10%, we compute the amount after 3 years:
A = 8,000 * (1.10)^3 = 8,000 * 1.331 = Rs 10,648Since this matches the given final amount, the principal value is confirmed to be correct.

Why Other Options Are Wrong:

• Rs 9,000, Rs 8,500, Rs 7,500, Rs 9,500: If you plug any of these into A = P * (1.10)^3, the resulting amount will not equal Rs 10,648. They represent typical estimation mistakes or confusion between simple and compound interest.

Common Pitfalls:
Common errors include using simple interest formula instead of compound interest, or forgetting to cube 1.10 correctly. Some test takers try to approximate mentally and end up with rounded values that do not match exactly. Always use the precise factor (1.10)^3 in such questions.

Final Answer:
The original principal amount invested was Rs 8,000.