You own a Futures contract that will settle in one month$*1.$ Yesterday$$s closing price for the underlying security was $$99\mathrm{.}70.$ The continuously compounded overnight$*2$ interest rate is $3\mathrm{.}6\%$ and today you have $$100$ in your margin account. The only interest rate is the overnight rate.

$($a$)$ What was the Futures Price at close yesterday? Assume this equals the Forward Price for an equivalent contract. How much cash do you have in your margin account at the end of the day in $2$ days, in each of the following cases:

see the following:

Maturity $($years$)1$

$2$

$3$

$4$

$5$

Face Value $$100$ $$100$ $$100$ $$100$ $$100$

Zero Rate Coupon $1\mathrm{.}00\%4\%$

$-6\%1\mathrm{.}50\%5\%1\mathrm{.}70\%3\%1\mathrm{.}75\%7\%$

Price Yield $--$ $$109\mathrm{.}00-$

$$110\mathrm{.}191\mathrm{.}42\%--$

$--$

$($b$)($c$)($d$)$

today tomorrow $$120$ $$110$

$$100$ $$100$ $$80$ $$90$

$2$ days $ $100$

$ $100$ $ $100$

Futures Price at close

You probably want to use $4$ decimal places to solve questions $($b$)-($d$).($e$)$ How would the answers above change if there was no interest rate?

$($f$)$ What are your conclusions from the answers obtained in $($b$)-($e$)?$

$*1$You may assume $1$ month $=30$ days, which means that $30$ days $=1$ of one year $12$

$*2$Essentially, that translates in every day being paid a $($continuous$)$ rate of $3\mathrm{.}6\%=0\mathrm{.}01\%=1$bp $12\backslash$times $30$