Please answer the following questions: #$1,$ #$2,$ #$3,$ and #$4$

$1.$ Given the following information, calculate the value of the Call option using the Black Scholes Model.

S $=14=$ Stock Price

X $=16=$ Exercise or Strike Price

r $=0\mathrm{.}05=$ Risk Free Rate

T $=0\mathrm{.}25=$ Time to Maturity $($as a fraction of one year$)$

N$($d$1)=0\mathrm{.}1469$

N$($d$2)=0\mathrm{.}1230$

$2.$ If a stock sells for $$100$ per share, its last dividend was $$1\mathrm{.}50$ and its growth rate is $5\%,$ what is the stock$$s required rate of return?

$3.($a$)$ Given the following information, calculate the company$$s internal growth rate. Return on Equity $=30\%$; Dividend Payout Ratio $=10\%.($b$)$ Please explain the significance of the calculated internal growth rate in terms of assessing the investment merits of this company.

$4.$ Brainteaser $/$ Thought Problem: Options are viewed as tools for helping to either reduce or hedge against price risk. However, the pervasive use of options is associated with increased rather than lower price volatility. Please explain this seeming paradox.