$51.$ What is the present value of your trust fund if you have projected that it will provide you

with $$50,000$ on your $30$th birthday $(7$ years from today$)$ and it earns $10\%$ compounded

annually?

A$.$ $$25,000\mathrm{.}00$

B$.$ $$25,657\mathrm{.}91$

C$.$ $$28,223\mathrm{.}70$

D$.$ $$29,411\mathrm{.}76$

$52.$ How much must be deposited today in an account earning $6\%$ annually to accumulate a

$20\%$ down payment to use in purchasing a car one year from now, assuming that the car's

current price is $$20,000,$ and inflation will be $4\%?$

A$.$ $$3,774\mathrm{.}61$

B$.$ $$3,782\mathrm{.}20$

C$.$ $$3,924\mathrm{.}53$

D$.$ $$4,080\mathrm{.}08$

$53.$ What is the present value of a four$-$year annuity of $$100$ per year that begins $2$ years from

today $($end of year $1)$ if the discount rate is $9\%?$

A$.$ $$297\mathrm{.}22$

B$.$ $$323\mathrm{.}97$

C$.$ $$356\mathrm{.}85$

D$.$ $$272\mathrm{.}68$

$54.$ A perpetuity of $$5,000$ per year beginning today is said to offer a $15\%$ interest rate. What

is its present value?

A$.$ $$33,333\mathrm{.}33$

B$.$ $$37,681\mathrm{.}16$

C$.$ $$38,333\mathrm{.}33$

D$.$ $$65,217\mathrm{.}39$

please explain with formulas :)