$55.$ How much must be invested today in order to generate a $5-$year annuity of $$1,000$ per

year, with the first payment $1$ year from today, at an interest rate of $12\%?$

A$.$ $$3,604\mathrm{.}78$

B$.$ $$3,746\mathrm{.}25$

C$.$ $$4,037\mathrm{.}35$

D$.$ $$4,604\mathrm{.}78$

$56.$ How much must be saved at the end of each year for the next $10$ years in order to

accumulate $$50,000,$ if you can earn $9\%$ annually? Assume you contribute the same amount

to your savings every year.

A$.$ $$3,291\mathrm{.}00$

B$.$ $$3,587\mathrm{.}87$

C$.$ $$4,500\mathrm{.}33$

D$.$ $$4,587\mathrm{.}79$

please explain with formulas? :)