Question

A perpetuity pays $2500 at the end of every month for 11 months of each year. At the end of the 12th month of each year, it pays double that amount. If the effective ANNUAL rate is 10.9%, what is the present value of this perpetual annuity? Tried these answers and they were incorrect: 312782.77, 298165.14 Please show steps!!!!

Answer 1

monthly interest rate {[1.109]^[1/12]}-1 = 0.86588% or 0.0086588

First of all bring all payments to the equivalent present value annual payment:

= {[2500/(1+0.0086588)^1]+ [2500/(1+0.0086588)^2]+ [2500/(1+0.0086588)^3]+ [2500/(1+0.0086588)^5]+ [2500/(1+0.0086588)^6]+ [2500/(1+0.0086588)^7]+ [2500/(1+0.0086588)^8]+ [2500/(1+0.0086588)^9]+ [2500/(1+0.0086588)^10]+ [2500/(1+0.0086588)^11]+ [5000/(1+0.0086588)^12]}

= $30,631.88

the present value of this perpetual annuity starting at t=1 is

Annual amount/effective annual interest rate

the present value of this perpetual annuity(starting at time t is equal to zero)= $30,631.88 + {$30,631.88/10.9%}

= $311,658.33