Questions CFA lvl 1 Curriculum first, specified, forever, continue

pawn

As discussed earlier, an annuity is a series of payments of a fixed amount for a specified number of periods. Suppose we own a perpetuity. At the same time, we issue a perpetuity obligating us to make payments; these payments are the same size as those of the perpetuity we own. However, the first payment of the perpetuity we issue is at t ? 5; payments then continue on forever. The payments on this second perpetuity exactly offset the payments received from the perpetu- ity we own at t ? 5 and all subsequent dates. We are left with level nonzero net cash flows at t ? 1, 2, 3, and 4. This outcome exactly fits the definition of an annuity with four payments. Thus we can construct an annuity as the difference between two perpetuities with equal, level payments but differing starting dates.
Can someone explain to me in layman term? I do not really get what it meant. Sorry I have no financial background… So please pardon me.

draz

ah ok I think I got it! Thanks. How come the curriculum need to explain until so difficult for people to understand. Sigh…

pennyless

@chibwack…I think to add to that ..c.an’t we just say “since the perpetuities are a wash starting in year 5, we only have to consider years 0-4”

Maddin

Basically what we have are two identical perpetuity’s with different start dates.  Lets say the payment is $5.  Then the payment stream looks like this:
T=0 $0 (assuming regular, not due)
T=1 +$5
T=2 +$5
T=3 +$5
T=4 +$5
T=5 +$5, -$5
T=6 +$5, -$5
…
Because we recieve the one perp starting today, and don’t start paying the second until t=5, we end up with fixed payments coming in up to T=4, or in other words is a regular annuity with four years to maturity and payments of $5, or the difference of the two perpetuities w/same payments and different start dates.