$39.$ What is the present value of $$100$ to be deposited today into an account paying $8\%,$

compounded semiannually for $2$ years?

A$.$ $$85\mathrm{.}48$

B$.$ $$100\mathrm{.}00$

C$.$ $$116\mathrm{.}00$

D$.$ $$116\mathrm{.}99$

$40.$ What is the present value of a five$-$period annuity of $$3,000$ if the interest rate per period

is $12\%$ and the first payment is made today?

A$.$ $$9,655\mathrm{.}65$

B$.$ $$10,814\mathrm{.}33$

C$.$ $$12,112\mathrm{.}05$

D$.$ $$13,200\mathrm{.}00$

$41.$ With $$1\mathrm{.}5$ million in an account expected to earn $8\%$ annually over the retiree's $30$ years

of life expectancy, what annual annuity can be withdrawn, beginning today?

A$.$ $$112,148\mathrm{.}50$

B$.$ $$120,000\mathrm{.}00$

C$.$ $$123,371\mathrm{.}44$

D$.$ $$133,241\mathrm{.}15$

please explain these with formulas :)