A sum of ₹ 40,000 was lent for one year at 16% per annum. If the same sum is lent for the same time and at the same rate percent but compounded half-yearly, how much more will the interest be ?

For compound annually:

P = ₹ 40,000, R = 16 %, T = 1 year

C.I. = P $\Big(1 + \dfrac{R}{100}\Big)^n$ - P

= 40,000 x $\Big(1 + \dfrac{16}{100}\Big)^1$ - 40,000

= 40,000 x $(1 + 0.16)^1$ - 40,000

= 40,000 x $(1.16)$ - 40,000

= 46,400 - 40,000

= ₹ 6,400

For compound half-yearly:

P = ₹ 40,000, R = $\dfrac{16}{2}$ % = 8 %, T = 1 x 2 = 2 years

C.I. = P $\Big(1 + \dfrac{R}{100}\Big)^n$ - P

= 40,000 x $\Big(1 + \dfrac{8}{100}\Big)^2$ - 40,000

= 40,000 x $(1 + 0.08)^2$ - 40,000

= 40,000 x $(1.08)^2$ - 40,000

= 40,000 x 1.1664 - 40,000

= 46,656 - 40,000

= ₹ 6,656

Difference between the compound interest = 6,656 - 6,400

= ₹ 256

Hence, the compound interest is ₹ 256 more when compounded half-yearly.