The difference between simple interest and compound interest on a sum of money for 1 year at 4% per 6 months is Rs.4. Find the sum?

Rs.2500

Rate = 4% per 6 months, so in 1 year there are 2 compounding periods.

For 1 year:

• Simple Interest (SI) $= P \times 8\%$
• Compound Interest (CI) $= P \left[(1.04)^2 - 1\right]$

Difference between CI and SI:

$P \left[(1.04)^2 - 1 - 0.08\right]$

$= P(1.0816 - 1 - 0.08)$

$= P(0.0016)$

Given the difference is ₹4:

$0.0016P = 4$

$P = \frac{4}{0.0016} = 2500$