5.7 The 4-year discount factor is 1/(1.08)4.7350. The 4-year annuity factor is [1/.08 - 1/(.08 x 1.084)] = 3.3121. This is the difference between the present value of a $1 perpetu- ity starting next year and the present value of a $1 perpetuity starting in year 5: PV (perpetuity starting next year)- 12.50 .08 1 1 -PV (perpetuity starting in year 5) X = 9.1879 .08 (1.08)4 =12.50-9.1879=3.3121 = PV (4-year annuity) which matches the annuity factor.