$1.$ You are making forecasts for two securities that promise perpetual, growing annual cash flows. For both securities$,$ calculate the cash flow you can expect at the end of year $7($that is$,$ seven years from now$).$

a$.$ Security A will pay $$10$ next year $($year $1),$ and the cash flows will grow at a rate of $2\%$ per year thereafter.

b$.$ Security B paid $$9$ last night, and the cash flows are expected to grow at a rate of $2\mathrm{.}5\%$ per year.

Answer Question $1$:$)$

For Security$-$A:

Year$-1\text{'}$s cash flows $=$ $$10\mathrm{.}0000[$First cashflow$]$

Year$-2\text{'}$s cash flows $=$ $$10\mathrm{.}2000[$$$10$ x $102\%=$ $$10\mathrm{.}2]$

Year$-3\text{'}$s cash flows $=$ $$10\mathrm{.}4040[$$$10\mathrm{.}2$ x $102\%=$ $$10\mathrm{.}404]$

Year$-4\text{'}$s cash flows $=$ $$10\mathrm{.}6121[$$$10\mathrm{.}404$ x $102\%=$ $$10\mathrm{.}6121]$

Year$-5\text{'}$s cash flows $=$ $$10\mathrm{.}8243[$$$10\mathrm{.}6121$ x $102\%=$ $$10\mathrm{.}8243]$

Year$-6\text{'}$s cash flows $=$ $$11\mathrm{.}0408[$$$10\mathrm{.}8243$ x $102\%=$ $$11\mathrm{.}0408]$

Year$-7\text{'}$s cash flows $=$ $$11\mathrm{.}26[$$$11\mathrm{.}0408$ x $102\%=$ $$11\mathrm{.}26]$

For Security$-$B:

Year$-0\text{'}$s cash flows $=$ $$9\mathrm{.}0000[$First cashflow$]$

Year$-1\text{'}$s cash flows $=$ $$9\mathrm{.}2250[$$$9$ x $102\mathrm{.}5\%=$ $$9\mathrm{.}225]$

Year$-2\text{'}$s cash flows $=$ $$9\mathrm{.}4556[$$$9\mathrm{.}225$ x $102\mathrm{.}5\%=$ $$9\mathrm{.}4556]$

Year$-3\text{'}$s cash flows $=$ $$9\mathrm{.}6920[$$$9\mathrm{.}4556$ x $102\mathrm{.}5\%=$ $$9\mathrm{.}692]$

Year$-4\text{'}$s cash flows $=$ $$9\mathrm{.}9343[$$$9\mathrm{.}692$ x $102\mathrm{.}5\%=$ $$9\mathrm{.}9343]$

Year$-5\text{'}$s cash flows $=$ $$10\mathrm{.}1827[$$$9\mathrm{.}9343$ x $102\mathrm{.}5\%=$ $$10\mathrm{.}1827]$

Year$-6\text{'}$s cash flows $=$ $$10\mathrm{.}4372[$$$10\mathrm{.}1827$ x $102\mathrm{.}5\%=$ $$10\mathrm{.}4372]$

Year$-7\text{'}$s cash flows $=$ $$10\mathrm{.}70[$$$10\mathrm{.}4372$ x $102\mathrm{.}5\%=$ $$10\mathrm{.}70]$

$2.$Assume that the appropriate discount rate for both perpetuities described in Question $1$ is $9\%.$ Calculate the present value of the expected future payments from each of these securities$.($please answer Question$2$ using the results of Question$1)$