Question

Assume the appropriate discount rate is 4%. You will receive a payment every year for the next 17 years, which will grow at 3% annually. The amount of the first payment will be $2,000. What is the current value of this series of payments?

Answer 1

PV of annuity for growing annuity
P = (PMT/(r-g)) x (1-((1+g)/(1 + r)) ^n)
Where:
P = the present value of an annuity stream	P
PMT = the dollar amount of first payment	$    2,000.00
r = the effective interest rate (also known as the discount rate)	4%
n = the number of periods in which payments will be made	17
g= Growth rate	3%
PV of series of payments=	(PMT/(r-g)) x (1-((1+g)/(1 + r)) ^n)
PV of series of payments=	(2000/(4%-3%)) * (1-((1+3%)/(1 + 4%)) ^17)
PV of series of payments=	$ 30,294.45