Compound amount after two years – UGC NET Question

For compound interest compounded annually, the amount A after n years is A = P(1 + R/100)^n. Substituting P = 5000, R = 10 and n = 2 gives A = 5000(1.1)^2 = 5000 × 1.21 = 6050. This includes both the principal and the accumulated interest over 2 years. Therefore, the amount after 2 years is ₹6050.

Option A:
₹6050 is correct because it reflects a 10% increase in the first year to ₹5500 and another 10% increase on ₹5500 in the second year, giving an interest of ₹550 in the second year. Adding the two years’ interest, 500 + 550 = 1050, to the principal yields 6050. This step-by-step reasoning confirms the formula-based calculation.

Option B:
₹6000 would correspond to a simple interest of ₹1000 over 2 years at 10% per annum, ignoring compounding in the second year. Compound interest, however, adds interest on both principal and accumulated interest. Therefore, 6000 underestimates the true amount.

Option C:
₹5900 is even smaller than the simple interest amount and thus significantly underestimates the effect of compound growth. It does not arise from any standard calculation with the given rate and time. Hence, this option is incorrect.

Option D:
₹6100 overestimates the compound amount at 10% per annum on ₹5000 for 2 years. It might result from an incorrect assumption of a higher effective rate. Since the exact formula yields 6050, 6100 cannot be accepted as correct.