At the start of each year, an investor invests 3,000 into a pension fund. The annual effective investment return earned over year n is denoted by the random variable in , for n = 1,2, ... It is assumed that {in), n = 1,2,... are independent and identically distributed. Let An be the accumulated value of the pension fund at the end of year n. Assume that Ao = 0. Derive a recursive formula for E[A] in terms of moments of An-1 and in. You do not need to derive a recursive formula for the first moment An-1 (a) (b) If E[in] = 0.05 and the standard deviation of in is 0.12, then E[A]] = 21,268,794,314 (you are not required to show this). (0) Calculate E[A, (ii) Hence calculate E[Aol. At the start of each year, an investor invests 3,000 into a pension fund. The annual effective investment return earned over year n is denoted by the random variable in , for n = 1,2, ... It is assumed that {in), n = 1,2,... are independent and identically distributed. Let An be the accumulated value of the pension fund at the end of year n. Assume that Ao = 0. Derive a recursive formula for E[A] in terms of moments of An-1 and in. You do not need to derive a recursive formula for the first moment An-1 (a) (b) If E[in] = 0.05 and the standard deviation of in is 0.12, then E[A]] = 21,268,794,314 (you are not required to show this). (0) Calculate E[A, (ii) Hence calculate E[Aol