$6.$ An investment offers $$25,000$ per year for $12$ years, with the first payment occurring one year from now. If the required return is $3\mathrm{.}15$ percent, what is the value of the investment?What would the value be if the payments occurred for $20$ years? For $50$ years? Forever?

$7.$ If you put up $$450,000$ today in exchange for a $5\mathrm{.}375$ percent, $30-$year annuity, what will the annual cash flow be$?$