Consider a growing annuity which pays out until time T a cash $$ow each period

growing at the constant rate of $1+$ g per period. Assume the rst payment C

occurs at the end of the rst period and that all cash $$ows are discounted using

a constant interest rate of r compounded per period.

Using the result in $($a$),$ show that the following is true:

PVAnnuity $=$

C

$1+$ r

$+$

C$(1+$ g$)$

$(1+$ r$)2+$

C$(1+$ g$)2$

$(1+$ r$)3++$

C$(1+$ g$)$T$1$

$(1+$ r$)$T

$=$ C

$"$

$1$

r $$ g $$

$(1+$ g$)$T

$($r $$ g$)(1+$ r$)$T

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