UGCNET Questions

Compound interest for 2 years at 10% per annum is computed using the amount formula A = P(1 + R/100) raised to the power of time. Here, A = 10,000 × (1 + 10/100)² = 10,000 × (1.1)². The value of (1.1)² is 1.21, so the amount becomes 10,000 × 1.21 = 12,100. The compound interest is the amount minus the principal, which is 12,100 − 10,000 = ₹2,100.

Option A:
Option A, ₹1,000, equals simple interest for one year at 10% but fails to account for the interest-on-interest effect in the second year. It underestimates the total interest earned over two years.

Option B:
Option B, ₹2,000, corresponds to simple interest over two years (10% each year on the principal only), but compound interest is slightly higher because the second year’s interest is also earned on the first year’s interest.

Option C:
Option C correctly derives the amount using the compound interest factor (1.1)² and subtracts the original principal. This procedure captures the compounding process and yields the slightly larger interest of ₹2,100.

Option D:
Option D, ₹2,200, overstates the effect of compounding and would require a higher effective rate or more time than actually given in the problem.

For compound interest, the amount is given by A = P(1 + R/100)ᵗ. Here P = 10,000, R = 5% and t = 2 years. This gives A = 10,000 × (1.05)². The square of 1.05 is 1.1025, so the amount becomes 10,000 × 1.1025 = ₹11,025. This includes both the original principal and the interest earned over two years.

Option A:
Option A, ₹10,500, represents the amount after one year of compound or simple interest at 5%, not two years. It misses the second period of compounding.

Option B:
Option B, ₹11,000, may come from incorrectly adding 5% of 10,000 twice and ignoring the interest on interest, which is the essence of compounding.

Option C:
Option C, ₹11,250, overestimates the effect of compounding and does not match the precise factor (1.05)². It might arise from using an incorrect growth factor.

Option D:
Option D uses the exact compounding formula and incorporates the second year’s interest on the first year’s interest. It therefore gives the correct accumulated amount of ₹11,025.