You are given a perpetuity that makes payments every two years, with a payment at the beginning of the year numbered 2n + 1, for n = 0, 1, 2, …, equal to 1/((n+1)(n+2)*3^{n}). Find the present value of this perpetuity at time 0, given that the annual effective interest rate is 4.5%.
i% = | 4.50% | |||
Keeping n= | 1 | |||
Payment is made at the beginning of | 2n+1= | 2*1+1= | 3 | yr |
Cashflow at the beginning of (2n+1= 3) year = | 1/((n+1)(n+2)*3n)= | 1/((1+1)(1+2)*3*1)= | 0.056 | |
PV of Perpetuity = | C/i% = | 0.056/4.5%= | 1.23 | |
This can be explained with a diagram (2n+1) yr |
0......................1.................2.....................3.....................n
PV=1.23 <................................................... C= 0.056
2n+1 means 3 yr keeping n as 1. Coupon Payment is made every 2 years ie in the begining of the 3 rd year. Cahslfow at begining of 3rd year or (2n+1)yr is 0.056. Calculating PV of perpetuity on this basis 1.23.
Get Answers For Free
Most questions answered within 1 hours.