Question

A growing monthly perpetuity will start 6 months from today. If the discount rate is 6% APR compounded monthly, what is the value of the perpetuity today (at time t=0) if the growth rate is 1.2% APR compounded monthly and the first payment is $100? *Round to the nearest $

Answer 1

Solution:

Effective annual discount rate=[1+(APR/no. of compunding in a year)]^no. of compounding-1

=[1+(0.06/12)]^12-1=0.062 or 6.2% per annum

Discount rate per month=6.2/12=0.52%

Effective annual growth rate=[1+(0.012/12)]^12-1=0.012 or 1.2%

Growth rate per month=1.2/12=0.1%

Present value of annuity at begining of 6th year=Anntuity/Discount rate-growth rate

=100/0.52%-0.1%

=$23809.52

Present value of annuity(Today)=$23809.52/(1+discount rate)^5

=$23809.52/(1+0.0052)^5

=$23,200