Question

A perpetuity pays $1000 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 10.4%, what is the present value of this perpetual annuity?

Answer 1

The perpetuity pays $1,000 for the first 11 months of each year and in the 12^th month, the perpetuity pays $2,000. Thus, it can be said that the perpetuity pays $1,000 per month and an additional $1,000 is paid at the end of each year. To determine the present value (PV) of perpetuity it is required to calculate the PV of both the perpetuity.

Compute the monthly interest rate, using the equation as shown below:

Monthly interest = Annual effective interest rate/ 12 months

                           = 10.4%/ 12 months

                           = 0.867%

Hence, the monthly interest rate is 0.867%.   

Compute the PV of the monthly receipts, using the equation as shown below:

PV = Monthly receipts/ Monthly rate

      = $1,000/ 0.867%

      = $115,340

Hence, the PV of monthly receipts is $115,340.

Compute the PV of annual receipts, using the equation as shown below:

PV = Annual receipts/ Effective annual rate

      = $1,000/ 10.4%

      = $9,615

Hence, the PV of annual receipts is $9,615.

Compute the present value (PV) of perpetuity, using the equation as shown below:

PV = PV of monthly receipts + PV of annual receipts

      = $115,340 + $9,615

      = $124,955

Hence, the PV of perpetuity is $124,955.