If interest is being compounded half yearly, then what sum will amount to Rs 51840 in 2 years at the rate of 40% per annum on compound interest?

Rs 25000

The rate of interest = 40% per annum

The amount = Rs 51840

Formula used: 

Amount = P x $[1+ (\frac{R}{100})]^2$

The effective time = 2 x 2 = 4 years

The effective rate of interest = $\frac{40}{2}$ = 20% half yearly

51840 = P x $[1+ (\frac{20}{100})]^4$

⇒ 51840 = P x $[\frac{6}{5}]^4$   

⇒ 51840 = P x $[\frac{1296}{625}]$     

⇒  P = $\frac{51840 \times 625}{1296}$

        =   25000

Thus, the sum is Rs 25,000