Question

You would like to purchase a delayed perpetuity, which pays $2400 every year. You would like this perpetuity to start 27 years later. The asset requires you to make the same deposit every year starting from today and end a year before the perpetuity starts. How much is the deposit every year? The interest rate is at 9%. (Round to Integer)

Answer 1

Perpetuity amount	2400
Interest rate	9%
PV of annuity=	2400/9%
PV of annuity=	$     26,667
So this amount has to be paid at the beginning of 27th year
FV of annuity
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
P = PMT x ((((1 + r) ^ n) - 1) / r)
Where:
P = the future value of an annuity stream	$     26,667
PMT = the dollar amount of each annuity payment	To be calculated
r = the effective interest rate (also known as the discount rate)	9%
n = the number of periods in which payments will be made	27
FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / r)
$                                                                                      26,667	PMT * ((((1 + 9%) ^ 27) - 1) / 9%)
Each annual payment=	26667/ ((((1 + 9%) ^ 27) - 1) / 9%)
Each annual payment=	$          260