$7.$ Professor$$s Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $$120,000$ at age $60,$ the firm will pay the retiring professor $$850$ a month until death. If the professor$$s remaining life expectancy is $30$ years. What is the effective annual rate $($EAR$)?$

$8.$ On the issue date, you bought a $30-$year maturity, $8\%$ semi$-$annual coupon bond. The bond then sold at YTM of $7\%.$ Now, five years later, the similar bond sells at YTM of $6\%.$ If you hold the bond now, what is your realized rate of return for the $5-$year holding period?

$9.$ Todd Co$.$ just paid dividends of $$5\mathrm{.}00($D$0)$ per share. These dividends are expected to grow at a $12\%$ rate for the next four years and at a $4\%$ rate thereafter $($forever$).$ What is the value of the stock if the appropriate discount rate is $10\%?$