The difference between the compound interest and the simple interest on Rs. 5000 for 2 years at 8% per annum, when interest is payable yearly, is to be found. What is the value of this difference in rupees?

Introduction / Context:
This question directly compares compound interest and simple interest on the same principal, rate, and time period. Because compound interest takes into account interest on interest, while simple interest does not, the compound interest is slightly higher for more than one year. The problem asks specifically for the numerical difference between the two types of interest over 2 years at 8 percent per annum on Rs. 5000.

Given Data / Assumptions:
Principal P is Rs. 5000.
Rate of interest r is 8 percent per annum.
Time period t is 2 years.
Simple interest and compound interest are both calculated on the same principal and rate.
Compound interest is compounded yearly.

Concept / Approach:
For simple interest, I_si = P * r * t / 100. For compound interest, with annual compounding, amount A = P * (1 + r / 100)^t and compound interest I_ci = A - P. After calculating both I_si and I_ci, we subtract to find the difference D = I_ci - I_si. Since the period is short and the rate is moderate, the difference will not be very large but still must be computed accurately.

Step-by-Step Solution:
Compute simple interest I_si on Rs. 5000 at 8 percent for 2 years.I_si = 5000 * 8 * 2 / 100 = 5000 * 16 / 100 = 800 rupees.Next, compute compound interest I_ci for the same principal, rate, and time.Amount A under compound interest is A = 5000 * (1 + 8 / 100)^2.Compute (1 + 8 / 100) = 1.08, so A = 5000 * (1.08)^2.Calculate (1.08)^2 = 1.1664, so A = 5000 * 1.1664 = 5832 rupees.Compound interest I_ci = A - P = 5832 - 5000 = 832 rupees.Difference between compound and simple interest is D = I_ci - I_si = 832 - 800 = 32 rupees.Thus the required difference is Rs. 32.

Verification / Alternative check:
One quick check is to compute interest year by year under compound interest. For the first year, interest is 5000 * 8 / 100 = 400 rupees, so amount becomes 5400 rupees. For the second year, interest is on 5400, which equals 5400 * 8 / 100 = 432 rupees. Total compound interest is 400 + 432 = 832 rupees. Simple interest for 2 years is 800 rupees as computed earlier. Difference remains 832 - 800 = 32 rupees, confirming the result.

Why Other Options Are Wrong:
Differences of Rs. 30, Rs. 31, or Rs. 33 are near the correct value but do not exactly match the computed difference of 32 rupees.
Rs. 35 is farther away and results from a larger miscalculation or from using an incorrect rate or time period.
Only Rs. 32 matches the correctly computed difference using standard formulas.

Common Pitfalls:
Errors often occur when squaring 1.08 or when multiplying by 5000. Some learners mistakenly compute the difference between amounts instead of between interests, although in this particular case the difference between amounts and between interests coincides because principal is the same. Mixing up rate or time can also lead to incorrect results. Clear stepwise calculation avoids these mistakes.

Final Answer:
The difference between compound interest and simple interest on Rs. 5000 for 2 years at 8 percent per annum is Rs. 32.