Compound Interest with Half-Yearly Compounding – Find time: In what time will ₹ 6,250 amount to ₹ 6,632.55 at 4% compound interest payable half-yearly?

Introduction / Context:
With half-yearly compounding, the annual rate is split into two equal periods. We can compare the required amount ratio to integer powers of the per-period factor to count how many half-year steps are needed, then convert to years.

Given Data / Assumptions:

• P = 6,250
• Nominal r = 4% per annum
• Half-yearly compounding ⇒ per-period rate = 2%
• A = 6,632.55

Concept / Approach:
Let n be the number of half-years. Then A/P = (1.02)^n. Compute A/P = 6,632.55 / 6,250 = 1.061208. Note that (1.02)^3 = 1.061208, so n = 3 half-years = 1.5 years.

Step-by-Step Solution:
A/P = 6,632.55 / 6,250 = 1.061208Per half-year factor = 1.02(1.02)^3 = 1.061208 ⇒ n = 3 half-yearsTime in years = 3 / 2 = 1.5 years

Verification / Alternative check:
Forward computation: 6,250 * (1.02)^3 = 6,250 * 1.061208 = 6,632.55 (matches exactly).

Why Other Options Are Wrong:
Other durations produce powers of 1.02 not equal to 1.061208, hence different amounts than ₹ 6,632.55.

Common Pitfalls:
Using 4% as the per-period rate would double the intended effect; always halve the rate and double the periods for half-yearly compounding.

Final Answer:
1.5 years