A sum of money amounts to ₹28,224 in 2 years and to ₹29,635.20 in 3 years when invested on compound interest, compounded annually. What is the sum of money?

₹25,600

Interest on Rs. 28224 = 29635.20 - 28224 = Rs. 1411.20

Rate of interest =\(\frac{1411.20}{28224}\) × 100

= 5%

Formula used-

Amount = P$(1 \;+\; \frac{R}{100})^t$

28824 = P [ 1 +  \(\frac{5}{100}\) ]²

28824 = P [ \(\frac{21}{20}\) ]²

28824 × \(\frac{20}{21}\)× \(\frac{20}{21}\) = P

P = 25600

So, Initial sum is Rs. 25600