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. Using both the simple interest and compound interest formulas, what is the value of this difference in rupees?

Introduction / Context:
This question compares compound interest and simple interest for the same principal, rate, and time, over a relatively short period of 2 years. Since compound interest allows interest to earn interest, it is slightly higher than simple interest for more than one year. The difference between these two is often asked in bank and finance related aptitude questions. Here, the principal is Rs 5000, the rate is 8% per annum, and the time is 2 years. The candidate must calculate both simple interest and compound interest accurately and then find their difference.

Given Data / Assumptions:

• Principal P = Rs 5000.
• Rate of interest R = 8% per annum.
• Time period T = 2 years.
• Interest is compounded annually for the compound interest case.
• Interest is calculated using simple interest for the simple interest case.

Concept / Approach:
Simple interest is given by:
SI = (P * R * T) / 100 For compound interest with annual compounding, the amount after T years is:
A = P * (1 + R / 100) ^ T Compound interest is then:
CI = A − P The required difference is:
Difference = CI − SI By computing SI and CI separately using these formulas and then subtracting, we can obtain the exact numerical difference in rupees.

Step-by-Step Solution:
Principal P = Rs 5000, R = 8% per annum, T = 2 years. First compute simple interest: SI = (5000 * 8 * 2) / 100. 8 * 2 = 16, so SI = (5000 * 16) / 100. 5000 * 16 = 80000. SI = 80000 / 100 = Rs 800. Now compute compound interest. Amount A = 5000 * (1 + 8 / 100) ^ 2 = 5000 * (1.08) ^ 2. (1.08) ^ 2 = 1.1664. A = 5000 * 1.1664 = 5832. Compound interest CI = A − P = 5832 − 5000 = Rs 832. Difference between CI and SI = 832 − 800 = Rs 32. Therefore, the required difference is Rs 32.

Verification / Alternative check:
We can verify by computing the compound interest stepwise. In the first year, interest at 8% on Rs 5000 is 400, so amount becomes 5400. In the second year, interest is 8% of 5400, which is 432, so the amount after 2 years is 5400 + 432 = 5832. Compound interest CI = 5832 − 5000 = 832, which matches our earlier calculation. Simple interest for 2 years is 2 * 400 = 800. The difference remains 832 − 800 = 32, so the result is confirmed.

Why Other Options Are Wrong:
Differences of Rs 30, Rs 31, Rs 33, or Rs 35 would require slightly different interest amounts or would arise from incorrect rounding of the compound amount. Since 8% and 2 years are exact and the calculations yield an exact difference of Rs 32, none of those other values is correct.

Common Pitfalls:
Some students approximate (1.08) ^ 2 incorrectly or forget to subtract the principal when finding compound interest. Others might mistakenly compute simple interest for only 1 year instead of 2 years. Confusing compound interest with simple interest and using the same formula for both is another common error. Following the formulas carefully and checking each step ensures a correct and accurate difference.

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