Question

Find the present value of a 20-year annuity with annual payments which pays $600 today and each subsequent payment is 5% greater than the preceding payment. The annual effective rate of interest is 10.25%.

Answer: 7851.19

Please show which equations you used and please do not use excel to answer this question.

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	To be computed
PMT = the dollar amount of each annuity payment	$    600.00
Next payment	$    630.00	600*105%
r = the effective interest rate (also known as the discount rate)	10.25%
n = the number of periods in which payments will be made	20
g= Growth rate	5%
PV of annuity=	(PMT/(r-g)) x (1-((1+g)/(1 + r)) ^(n-1))
PV of annuity=	(630/(10.25%-5%)) * (1-((1+5%)/(1 + 10.25%)) ^(19))
PV of annuity of payment from t1 to t19 at T0=	7251.19
PV of annuity stream=	600+7251.19
PV of annuity stream=	$ 7,851.19