I'll give a hint for (a) and (b):
(a) Create an equation for the balance of the fund in terms of the initial value, interest rate and the award.
Do this for F1, F2... until you can identify a pattern with the balance (You should see a geometric progression), and make a general equation for the nth solution (Fn).
(b) Using the equation for the nth year (Fn) carefully expand the GP until you get Fn to equal RHS.