Company KBM$\text{'}$s internal analysis indicates that the USD's gain in value over the EUR is coming to an end. However, the futures market for EUR$/$USD does not indicate the level of change that KBM is forecasting. Company KBM has decided to invest $30,000,000$ USD into an investment plan. KBM will purchase a put option and then deposit cash into high grade $4-$year EUR deposit accounts earning $5\mathrm{.}85\%$ compounded annually, the current spot rate is $1\mathrm{.}05$ EUR$/$USD$.$ A EUR $4-$year put option for $1\mathrm{.}08$ costs $3\mathrm{.}25\%$ of the USD deposit. For comparisons, KBM company can earn $5\mathrm{.}75\%$ in similar USD accounts.

a$.$ How much will KBM have to pay for the option? $3$ Points

b$.$ How much in EUR will KBM initially deposit after paying for the cost of the option? $3$ Points

c$.$ How much will KBM have in the EUR deposit account at the end of $4$ Years? $3$ Points

d$.$ How much in USD would KBM have if it had invested in similar USD accounts? $3$ Points

e$.$ If the dollar weakens to $1\mathrm{.}145$ EUR$/$USD how much would KBM have in USD when converting the EUR deposit accounts after the $4$ years? $3$ Points

f$.$ If the dollar stays strong at $1\mathrm{.}05,$ what is the value of the investment $($in USD$)$ after the $4$ years $($does the option get used$)?3$ Points