$2.$ Regeneron $($REGN$)$ is a non$-$dividend paying stock with a spot price of USD$950$ per share. An investment manager seeks to benefit from a rise in REGN$$s share price over the next six months and contracts with a bank for a six$-$month forward purchase of $1,000$ shares. Assume a risk$-$free rate of $4\mathrm{.}25\%$ and a flat yield curve.

a$.)$ What is the REGN six$-$month forward price?

b$.)$ The bank imposes a daily cash collateral requirement on the investment manager equal to the greater of USD$100,000$ or $100\%$ of the mark$-$to$-$market on the forward position. What is the collateral requirement at the inception of the trade, and how does it change in three months if the spot price of REGN falls to USD$845?$