Question

6. Given a 6 percent discount rate compounded quarterly, what is the present
value of a perpetuity of $100 per month if the first payment does not begin until the end
of year five?

Could you explain the question in detail with formula plz! I don't understand others poster answers.

Answer 1

Annual Rate Given =6% (Compounded Quarterly Rate)
Rate per quarter =Annual Rate/4 =6%/4 =1.5%

Since the perpetuity is monthly payment we need to calculate monthly rate
Since in a quarter there are 3 months hence
Monthly Rate formula =(1+Rate Per quarter)^(1/3)-1 =(1+1.5%)^(1/3)-1 =0.497520627265247%

Since the perpetuity begins at year 5
The value of Perpetuity at end of year 5 =PMT/Monthly Rate+PMT (Since Perpetuity begins at start of month)
=100+100/0.497520627265247% =20199.6691

Number of Months =5*12 =60
PV of Perpetuity today =The value of Perpetuity at end of year 5/(1+r)^5
=20199.6691/(1+0.497520627265247%)^60 =14997.66