$2.$ Given: interest rates are $6\%$ in the U$.$S$.$ and $15\%$ in the U$.$K$.$ The spot exchange rate for British pounds is $1\mathrm{.}27$ $$/$ and the $1-$year forward rate is F$1-$yr $=1\mathrm{.}19$ $$/.$ You wish to borrow dollars.

a$.$ How can you effectively $($synthetically$)$ borrow $$100,000$ for one year without using the U$.$S$.$ money market? $($List each transaction you would make including the amounts of each currency involved. You may use either continuous compounding or discreet compounding as long as you show your calculations.$)$

b$.$ What is the implied interest rate on your synthetic loan?

c$.$ Should you borrow directly or synthetically, and why?

d$.$ How could an arbitrageur make a risk$-$free profit?