Question

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)*3ⁿ). Find the present value of this perpetuity at time 0, given that the annual effective interest rate is 4.5%.  

Answer 1

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.