$$Want to have $$50,000$ in $15$ years.

$$Plan to deposit equal amount each year $($end$),$ which will

earn $7\%$ p$.$a$.$

$($a$)$ How much must you deposit annually?

$($b$)$ If you decide to make a lump$-$sum deposit today instead, how

large should this lump$-$sum deposit be$?$

$($c$)$ If you will receive $$10,000$ and deposit at the bank at the end of

year five, how much must you deposit annually?