Question

Problem #4: A perpetuity pays $3900 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 10.5%, what is the present value of this perpetual annuity? Problem #4: Answer correct to 2 decimals.

Answer 1

The perpetuity contains two perpetual annuities-

1. $3,900 at the end of every month
2. $3,900 at the end of every year.

Effective annual interest rate (EAR) of 10.5% is equivalent to monthly rate of 0.835516% as follows:

Monthly rate= [(1+EAR)^(1/12)]-1     = (1.105^0.083333)-1   = 0.835516%

Present value of perpetuity= PMT/r

Where PMT=periodical payment and r= rate of interest for the period.

Present value of the monthly annuity = $3,900/0.00835516 = $466,777.66

Present value of yearly annuity=$3,900/0.105 = $37,142.86

Therefore, total present value of the perpetuity= $466,777.66 + $37,142.86 = $ 503,920.51