Question

# You are given a perpetuity that makes payments every two years, with a payment at the...

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%.

 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.

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