What rate per cent per annum compound interest will Rs. 3,000 in 3 years if the interest is reckoned half yearly?

∵ 3000 = 2000(1 + r/200)⁶
⇒ 3/2 = (1 + r/200)⁶
⇒ 1 + r/200 = (3/2)^1/6
⇒ log(1 + r/200)= 1/6(log 3 - log 2 )
⇒ log(1 + r/200)= 1/6(0.4771-.3010)
= 0.02935
⇒ (1 + r/200) = antilog(.02935)
⇒ 1 + r/200 = 1.070 = 1 + 7/100
∴ r = 14%