Q$2.$ FX Rates and Interest Rates

Your boss tells you she needs to know the six$-$month $(6-$month$)$ euro interest rate$-$right away. You go to the Bloomberg... it is down. You go to the Internet to find "euro" on Yahool Finance... the company's network is down. You have thrown away your copy of the day's National Post. The company's subscription to The Wall Street Journal and Financial Times has lapsed. $($Remember Murphy's law.$)$

Fortunately, your company had a transaction in curo today, and your company's treasury department has obtained quotes of the spot and six$-$month forward rates $(\frac{\text{\$}}{E})$ from the bank as shown below. $($Well$,$ there is hope.$)$ Your colleague there could also find the six$-$month Eurodollar interest rate $($annualized$,$ simple interest$)$ below. You remember that one of your professors back in B$-$School insisted that the Eurocurrency money markets and the foreign exchange markets are quite efficient$-$at least for the major currencies$-$so that an arbitrage relation can be expected to hold across them. Armed with this knowledge, you quickly estimate the euro interest rate $($annualized$,$ simple interest$)$ for your boss. What is your estimate? Be sure to prorate the interest rates for the relevant period in your calculation. You, of course, know that the above "six$-$month Eurodollar interest rate" is the annualized rate for a six$-$month transaction, just as the $20-$year mortgage rate on your $($future$)$ home loan is the yearly rate that you will pay over the next $20$ years.

$\backslash$table$[[,,,],[$Spot rate $(\frac{\text{\$}}{}$lon$),1\mathrm{.}2078,$Euro interest rate $($annual$),],[6-$month forward rate $(\frac{\text{\$}}{}$lon$),1\mathrm{.}2025,,],[$$ interest rate $($annual$),0\mathrm{.}021,(-2\mathrm{.}10\%),]]$