A sum of ₹10000 amounts to ₹11664 in 2 years, at a certain rate percent per annum, when the interest is compounded yearly. What will be the simple interest on the same sum for $$5\frac{2}{5}$$ years at the same rate?

with the given information we can say that 

A=P$$(1+r\div{100})^{n}$$

where n is the time for which the amount is invested

applying this we get

11664=$$10000\times{\frac{(100+r)}{(100)}}^{2}$$

so we get 

$$108^{2}$$= $$(100+r)^{2}$$ 

removing the square from both the sides we get 

108 = 100+r

therefore r=8

 so now for simple interest we know

SI= $$PRT\div{100}$$

SI= $$(10000\times{8}\times\frac{27}{5})\div{100}$$

SI=4320