Question

A perpetuity pays $1800 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 11.5%, what is the present value of this perpetual annuity? I tried solving it this way but got it wrong: PV = [1800/(11.5%/12)] + [1800/11.5%] = $203 478.26

Answer 1

For n = 11 months, amount paid = X = $1800

For 12 month, amount paid = 2X = $3600

Monthly Interest rate = r = 0.115/12

Present Value of all the payments for 1st year = P

=> P = X/(1+r) + X/(1+r)² + .... X/(1+r)¹¹ + 2X/(1+r)¹² = X[1- (1+r)^-11]/r + 2X/(1+r)¹² = 1800[1- (1+0.115/12)^-11]/(0.115/12) + 3600/(1+0.115/12)¹² = $21917.91

Value of perpetuity if amount Z is paid each year = Z/r

=> Value of Perpetuity = P + P/r = 21917.91 + 21917.91/0.115 = $212,508.43