$57.$ Approximately how much should be accumulated by the beginning of retirement to

provide a $$2,500$ monthly check that will last for $25$ years, during which time the fund will

earn $6\%$ interest with monthly compounding?

A$.$ $$361,526\mathrm{.}14$

B$.$ $$388,017\mathrm{.}16$

C$.$ $$402,766\mathrm{.}67$

D$.$ $$414,008\mathrm{.}24$

$58.$ The salesperson offers, "Buy this new car for $$25,000$ cash or$,$ with an appropriate down

payment, pay $$500$ per month for $48$ months at $8\%$ interest, compounded monthly." Calculate

the "appropriate" down payment.

A$.$ $$1,000\mathrm{.}00$

B$.$ $$4,519\mathrm{.}04$

C$.$ $$5,127\mathrm{.}24$

D$.$ $$8,000\mathrm{.}00$

explain with formulas :)