Question

2

Un gusted basis since market prices should (2) Consider a ten-year annuity. $4,000 per year for 7 years is paid starting two years ago. $6,000 per year is paid over the remaining 3 years. Assume that the appropriate discount rate is 7% for all cash flows. only nen) Show a time line of cash flows. Assume that it is time 0 now. (a) What is the value of the entire annuity at time -2 when the 1st payment was made? (b) What is the value of the annuity at the start of year 7 (time of last payment)? (c) What is the value of the annuity at time zero?

Answer 1

2. a) PMT =4000
Number of years =7
Rate=7%
PMT for remaining 3 years =6000
Rate =7%
Value at time -2 =PMT*((1-(1+r)^-n)/r)+PMT*((1-(1+r)^-n)/r)/(1+r)^7
=4000*((1-(1+7%)^-7)/7%)+(6000/((1-(1+7%)^-3)/7%)/(1+7%)^7=31362.91

b)Value of at start of 7th year =PMT2/(1+r) =6000/(1+7%) =5607.48

c)Number of Periods for PMT 4000 =5 years

Value at time 0 =PMT*((1-(1+r)^-n)/r)+PMT*((1-(1+r)^-n)/r)/(1+r)^7
=4000*((1-(1+7%)^-5)/7%)+(6000/((1-(1+7%)^-3)/7%)/(1+7%)^5=27627.40