Financial Mathematics: Nonlevel annuities using geometric

Let i = 7% and v = 1+ i In each part, show annuity payments on a timeline to describe the given sums as the value of that annuity at a certain point in time. In other words, visualize the sums as present/future value of certain annuities. Then compute them using the geometric summation formula 1 - pn+1 s pk = 1+r+p2 +p3 + ... + p = 1-p k=0 Hint: Factoring out the first term of a geometric sum helps to rewrite it in the standard form above. (a) v + v10 + v11 + ... +223 = (b) v + v10 + v11 + ...= (c) 19 +v11 + v13 + ... + 123 = (d) (1 + i)23 + (1+i)22 + (1+i)21 +...+(1+i)! = (e) (1 - i)(1+i)23 + (1 - i)?(1 + i)22 + (1 - i)(1+i)21 + ... + (1 - i)23(1+i) =