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Task: Consider the present value an] of an annuity which consists of a series of n annual payments of 1 in arrear. The effective annual interest rate i is constant. Derive a formula to express an] in terms of vP and i, where v = (1+i)=?. Answer: The present value of a payment of one pound at time [Select] is v'. Hence that value of the annuity is (Select ] , which can be simplified to [ Select] 3 Therefore an] is equal to [ Select] (4) > [Select] [Select] 0 t t is (Select] [Select] 1 + v + ... + (n - 1) 1 + V + ... + van v+v^2 + ... + v^(n-1) + V + y^2 + ... + van I > [ Select] [Select] (v^n-1)/(v-1) (v^(n+1)-1)/(v-1) (v^n-v)/(v-1) v (v^n-1)/(v-1) [Select] [Select] (1 - v^n) /i (1 - van) / d 1 - V^(n-1) / 1 - v^(n-1) / d