Question

A perpetuity pays $2100 at the end of every month for 11 months of each year. At the end of the 12 th month of each year, it pays double that amount. If the effective ANNUAL rate is 11.6%, what is the present value of this perpetual annuity?

Answer 1

The present value of the described perpetuity is $235,344.83, calculated by summing the annual payments and dividing by the effective annual interest rate of 11.6%.

Step-by-step explanation:

To calculate the present value of a perpetuity with variable payments, we would use the present value formula for perpetuities and adjust for the increased payment in the 12th month. The perpetuity pays $2,100 monthly for 11 months and then $4,200 (double the monthly payment) at the end of the 12th month each year.

First, we find the annual payment summing up all the monthly payouts: $2,100 * 11 months + $4,200 = $27,300. Next, we use the formula for the present value of a perpetuity PV = C / r, where C is the annual cash flow and r is the annual discount rate.
Since the annual effective rate is 11.6%, we have r = 0.116. Therefore, the present value of this perpetuity is PV = $27,300 / 0.116 = $235,344.83 (rounded to two decimal places).