handwritten please

Question 3 a. Derive the following: i. the present value of an annuity payable pthly in advance; ii. the future value of an annuity due; iii. the present value of an increasing annuity in arrear; iv. the present value of a decreasing annuity due. [6] [5] [5] b. Suppose that the first payment of some annuity is P, the second payment being P+Q, the third being P+2Q and so on until a total of n payments are made. Derive an expression [5] for the present value of such a payment series assuming that the payments are made in arrear