3.12 Suppose the spot rates of interest for invest- ment horizons of 1 to 5 years are 4%, and for 6 to 10 years are 5%. (a) Compute the forward rates of interest in for t=1,2,., 10. (b) Calculate the present value of an annuity- immediate of $100 over 10 years. (c) Compute the future value of the annuity- immediate at the end of year 10, assuming future payments earn the forward rates of interest, using equation (3.18). (d) Repeat part (c) using equation (3.14). You should get the same answer as in part (c). (e) Show that the future value of the annuity- immediate at the end of year 10, assuming future payments earn the spot rates of inter- est as at time 0, is 100 ~ (ST010.05 - $50.05) + 100 x 8510.04 (f) Solve the problem in (e) numerically using the formula in Exercise 3.11. Do you get the same answer as using the formula in (e)? $77 = (1+2,9" am = (1 + 1)" (1+i;) 1 (3.18) 8] = + ---- +1 +1 (1 + if) j=t+1 = [(1 + i)(1+i)... (1+)] + [(1 + i)(1+i) ... (1+i)] + ... ... + (1+1)+1. (3.14)