A sum of money amounts to ₹4,624 in 2 years and to ₹4,913 in 3 years at a certain rate of interest, when interest is compounded per annum. The sum is _______.

₹4,096

Difference b/w amount with CI after 2 and 3 years = 4913 - 4624 = 289

Rate of interest = \(\frac{289}{4624}\) × 100%

= 6.25%

Now,

Let initial sum = P

P × [ 1 + \(\frac{6.25}{100}\) ]× [ 1 + \(\frac{6.25}{100}\) ] = 4624

P × [ 1 + \(\frac{1}{16}\) ]× [ 1 + \(\frac{1}{16}\) ] = 4624

P = 4624 × \(\frac{16}{17}\) × \(\frac{16}{17}\)

= Rs. 4096