The difference between the C.I and S.I on Rs 8000 for 3 years is Rs 61 .find rate

imple Intrest = pnr/100 = 8000×3×r/100 = 240r

Let us calculate compound intrest every year

end of first year intrest = 8000×r/100 = 80r

end of first year Amount = (8000 + 80r)

end of second year inrest = (8000+80r)×(r/100) = 80r + (8r^{2}/10)

end of second year Amount = 8000+160r + (8r^{2}/10)

end of third year intrest = [ 8000+160r + (8r^{2}/10) ]×(r/100) = 80r + (160r^{2} /100 ) + (8r^{3} /1000)

end of third year amount = 8000+240r + (240r^{2}/100) + (8r^{3} /1000)

hence compound intrest after 3 years = 240r + (240r^{2}/100) + (8r^{3} /1000)

difference between Simple intrest and Compound Intrest = (8r^{3} /1000) + (240r^{2}/100) = 61

difference = 8r^{3} + 2400r^{2} = 61×1000 or r^{3} + 300r^{2}= 61×125 = 7625 …(1)

put r =1 , LHS of eqn.(1) = 301 ≠ RHS

put r =2 , LHS of eqn.(1) = 1208 ≠ RHS

put r =3, LHS of eqn.(1) = 2727 ≠ RHS

put r =4 , LHS of eqn.(1) = 4864 ≠ RHS

put r =5 , LHS of eqn.(1) = 7625 = RHS

hence rate of intrest = 5%