Assume that the force of interest is constant over time. Let the constant force of interest be d and the equivalent effective rate of interest and discount be i and d, respectively. (a) Express 8 in terms of i. (b) Express d in terms of d. (c) By using the Taylor's expansion -1)k-12k x2 X3 In(1+x) = = + x4 + 4 k 2 3 k=1 and the expressions in (a) and (b), show that 22 d2 8 1 [i+d 2 1 23 + d3 24 d4 + 3 4 .] 2 The formula above shows that d is very close to the average of i and d