IFoA April 2009 Q10 (iii)

Can anyone check the solution of (iii)'s last part? Why are they taking V(S)=V(N).E(Y^2) = 500*E(Y^2) = 500*24398.3967?? Should not it be V(S) = (E(Y))^2.V(N)+E(N).V(Y)? I have understood the entire question just stuck at the end. Can anybody quickly confirm whether the last line of the solution is wrong or not?

 

Thank you sir! I was thinking even by using the generalized formula of V(S) = [E(Y)]^2*V(N)+V(Y)*E(N), I should have got the same answer as given in the solution, and hence asked this question. Later I discovered, while finding out E(Y^2), I mistakenly used the value of V(X) and E(X^2) and hence my answer did not match. I have rectified it then.