Question 3 [12 marks]. Suppose you decide to model interest rates by using the Varying Interest Rate model where R; is the effective interest rate for a deposit between time i and time i +1 and the R; are an i.i.d. sequence {R}}i=0,1,2,... of random variables with common distribution R; 5% with probability 0.4, 6% with probability 0.6. = (a) If 100 is deposited at time i 0, then what is the expected value of the deposit at time i = 4? Derive the result and then state it to the nearest pence. (b) Suppose you deposit 100 at time i 0 and another 100 at time i 1. Determine the expected value of the money accumulated at time i = 2. Derive the result and then state it to the nearest pence