Question

Calculating Annuity Present Value: An investment offers $5500 per year for 15 years, with the first payment occurring one year from now. If the required return is 7.5%, what is the value of the investment? What would the value be if the payments occurred for 40 years? 75 years? Forever?

Answer 1

PV of annuity = P(1-((1+r)^-n))/r

r	0.075
n	15
P	$5500
PV	?

Where r is the rate and n is the number of period. P is the payment per period

Substituting values we have:

Present Value=5500*(1-((1+0.075)^-15))/0.075

=$48,549.16

For 40 years:

Present Value=5500*(1-((1+0.075)^-40))/0.075
$69,269.25

For 75 years:

Present Value=5500*(1-((1+0.075)^-75))/0.075

$73,009.99

For forever we need present value of perpetuity:

PV perpetuity=Cash flow/rate
=$5,500/0.075

=$73,333.33