$1.$ Suppose the spot exchange rate between the U$.$S$.$ dollar and the Guatemalan quetzal is EGTQ$/$USD $=8,$ and spot rate between the U$.$S$.$ dollar and the Honduran lempira is EHNL$/$USD $=24.$

$($a$)$ Suppose that EHNL$/$GTQ $=4.$ If you hold U$.$S$.$ dollars, explain how you can exploit an arbitrage opportunity? To simplify, suppose you have $$100$ USD, explain how you can convert this into $$133\mathrm{.}33$ USD with zero risk, using the given exchange rates.

$($b$)$ In the absence of arbitrage opportunities, what must be the spot exchange rate between the Guatemalan quetzal and the Honduran lempira: EHNL$/$GTQ$?$

$2.$ Suppose the $1-$year nominal interest rate on the Korean won $($KRW$)$ is $3\mathrm{.}5\%$ and on the U$.$S$.$ dollar $($USD$)$ is $5\%.$ The spot exchange rate is $1300$ won per dollar. There is no risk premium.

$($a$)$ Compute the expected won$/$dollar exchange rate one year from now $($state your answer to two decimal places$).$

$($b$)$ Suppose the interest rate on the U$.$S$.$ dollar increases from $5\%$ to $6\%$ and the expected won$/$dollar exchange rate does not change $($take the answer from $($a$)$ as the starting point$).$ What happens to the spot won$/$dollar exchange rate $($state your answer to two decimal places$)?$ Compared to the spot rate in part $($a$),$ does this correspond to an appreciation or a depreciation of the Korean won?

$3.$ Suppose the interest rate in New Zealand is $0\mathrm{.}04$ and the interest rate in Costa Rica is $0\mathrm{.}05.$ The New Zealand dollar $($NZD$)$ is expected to purchase $350$ Costa Rican col $$on $($CRC$)$ in the future and the NZD has a risk premium of $0\mathrm{.}01.$ What is the spot exchange rate that satisfies UIP $($state your answer to two decimal places$)?$

$4.$ Suppose the interest rate in South Korea is $0\mathrm{.}04$ and the interest rate in Japan is $0\mathrm{.}03.$ The Japanese yen $($JPY$)$ can purchase $8\mathrm{.}2$ South Korean won $($KRW$)$ in the spot market and is expected to purchase $8$ units in the future. Based on UIP, which country has a riskier currency and what is the risk premium $($state your answer to two decimal places$)?$