Calculus is needed. A perpetuity-due has a payment once every k years. The j-th payment is j. Show that this perpetuity has present value equal to 1 ia- ani An annuity-immediate with payments once every k periods and a j-th payment of j has present value ai k Taking the limit as n approaches infinity of this expression gives the present value of a perpetuity-immediate. .vn lim ishi 1 iai isi 1 = Z opisali 1 ( 1)*(22:32 To convert this to a perpetuity-due, multiply by (1 + i)k. 1 1 2 1 Zanikli 1 ia Kli Calculus is needed. A perpetuity-due has a payment once every k years. The j-th payment is j. Show that this perpetuity has present value equal to 1 ia- ani An annuity-immediate with payments once every k periods and a j-th payment of j has present value ai k Taking the limit as n approaches infinity of this expression gives the present value of a perpetuity-immediate. .vn lim ishi 1 iai isi 1 = Z opisali 1 ( 1)*(22:32 To convert this to a perpetuity-due, multiply by (1 + i)k. 1 1 2 1 Zanikli 1 ia Kli