$8.$ The following exchange rates exist on a particular day.

Spot exchange rate: $$2/$

Forward exchange rate $(90$ days$)$: $$2/$

The following $($annualized$)$ interest rates on $90-$day government bonds also exist on this day:

Pound$-$denominated bonds: $4\%$

U$.$S$.$ dollar$$denominated bonds: $3\%$

Start with $20$ million US $$.$

a$.$ Is there any opportunity for arbitrage gain? Compare the return on covered investments in terms of US $ in $3$ months$$ time.

b$.$ Assume that there is no borrowing constraint, that is$,$ you can borrow whatever amount of money you want. How can you use this opportunity? Discuss it with an investment of a $20$ million US $ in mind.