Question

What is the value of a perpetuity today if my first payment of $1,500 starts in 8 years at 5%.

We know the answer is PV=21320.44. If you could show your work with the formula, it would be appreciated. Thanks!

Answer 1

PV of perpetuity is given by the formula: CF/r.
Where
CF = the periodic perpetual cash flow
r = the interest rate per period
But, it will the PV of the perpetuity at the
beginning of the first year at the end of which
the first payment is received.
So, if the formula, in this case, will give the
discount value of the perpetuity at the the
beginning of the 7th year. This is so because,
the payment will start in 8 years, which means
end of year 7.
The discounted value so got is to be discounted
further for 7 years to get the PV.
Now,
Discounted value at EOY 7 = 1500/5% =	$   30,000.00
PV of $30000 = 30000/1.05^7 =	$   21,320.44