Compound interest crediting frequency — yearly vs half-yearly for 1 year: What is the difference between the compound interest on ₹ 50000 at 12% per annum for one year when interest is credited yearly versus half-yearly?

Introduction / Context:
Compound interest depends on crediting frequency. For the same nominal annual rate and a one-year horizon, half-yearly compounding yields a slightly higher amount than yearly compounding.

Given Data / Assumptions:

• Principal P = ₹ 50000
• Nominal annual rate r = 12%
• Time = 1 year
• Compare yearly compounding vs half-yearly compounding

Concept / Approach:
Yearly CI amount A_y = P * (1 + r)^1 with r = 0.12. Half-yearly CI amount A_h = P * (1 + r/2)^2 with r/2 = 0.06. The difference is (A_h − A_y).

Step-by-Step Solution:
A_y = 50000 * 1.12 = ₹ 56000 → CI_y = ₹ 6000A_h = 50000 * (1.06)^2 = 50000 * 1.1236 = ₹ 56180 → CI_h = ₹ 6180Difference in CI = 6180 − 6000 = ₹ 180

Verification / Alternative check:
Effective annual rate with half-yearly compounding: (1.06^2 − 1) = 0.1236 = 12.36%. 12.36% of 50000 is ₹ 6180, confirming the difference of ₹ 180 versus 12% yearly (₹ 6000).

Why Other Options Are Wrong:
₹ 360 and ₹ 600 overstate the frequency effect; ₹ 240 and ₹ 500 do not match the exact calculation with 12% and a 1-year term.

Common Pitfalls:
Applying the 12% to two half-year periods without compounding (that would still be 12%). Correct handling requires multiplying by 1.06 twice.

Final Answer:
₹ 180