If the current exchange rate is US$1 equals 1.25 Euros, how much did you win in US dollars?
Here we just need to convert euros to dollars based on the exchange rate:
$1 = 1.25 Euros
x = 1 million Euros
x = (1,000,000) / 1.25
x= $800, 0000
Suppose that the interest rate in Irish banks is 5% for a one year CD. In the USA, the rate is 2% for a one year CD. If you left your winnings in Ireland, how many Euros would you have in a year?
We assume that the exchange rate is not changed in one year (they didn’t state any change in the question) Now if we leave our winnings in Ireland for a year; at the end of the year we would have:
1,000,000 * (105/100) = 1, 050, 0000 euros
If you had taken your winnings back to the USA, how many dollars would you have?
This time we should calculate our interest according to the U.S rates (2%). But first we need to convert or money into dollars. In the first question we found that 1,000,000 euro equals to $800,000. Thus at the end of the year we would have:
$800,000 * (102/100) = $816,000
Suppose when you cashed in your CD in Ireland a year from now, the exchange rate had changed from US$1 to 1.25 Euro, to US$1 to 1.30 Euro. How much would your Irish bank account be worth in US$ at that point?
We need to calculate both situations in order to compare them. In Ireland we would have
1, 050, 0000 euros at the end of the year (as calculated in the second part). However the exchange rate also changed.
$1 = 1.3 Euros
x = 1, 050, 0000 euros
x = (1, 050, 0000)/1.3
So our Irish bank account would worth $807,692
Did you do better off leaving your winnings in Ireland or bringing them home to the USA?
If we would keep the money in U.S, we would have 816,000 at the end of the year. So
leaving our winnings in Ireland was not a good decision.
Explain how banks and individuals can use “covered interest arbitrage” to protect themselves when they make international financial investments.
Banks and individuals borrow a currency, convert it to a second currency where it is invested, and sell this second currency forward against the initial currency. Thus riskless profits can be derived from discrepancies between interest differentials and the percentage discount or premium between the currencies involved in the forward transaction. Covered interest arbitrage is based on disequilibrium in interest rate parity.
Using the theory of purchasing power parity, explain how inflation impacts exchange rates.
The theory of purchasing power parity states that the exchange rate between one currency and another is in equilibrium when their domestic purchasing powers at that rate of exchange are equivalent. Let’s give an example. Assume that in the beginning prices for every good in U.S and Ireland is same and $1 equals to 1 euro and our euro to dollar exchange rate is 1. Suppose that Ireland has a 50% inflation rate whereas U.S has no inflation whatsoever. Now the price of a good in Ireland would increase 50% but the price of the same (identical) good in U.S would be the same. Thus $1 must equal to 1.5 euro and our euro to dollar exchange rate increase from 1 to 1.5 on foreign exchange markets. As we can see in the example, if two countries have different rates of inflation, then the relative prices of goods in the two countries will change. The relative price of goods is linked to the exchange rate through the theory of purchasing power parity. As we have seen, purchasing power parity tells us that if a country has a relatively high inflation rate, then the value of its currency declines.
Based on the theory of purchasing power parity, what can we infer about the difference in inflation between Ireland and the USA during the year your lottery winnings were invested? Show all calculations
In the beginning the exchange rate was US$1 equals 1.25 Euros. So we can say that the inflation rate in Ireland is (1.25-1)/1 = 25% higher than the inflation rate in U.S. During the year our lottery winnings were invested, the exchange rate changed to US$1 to 1.30 Euro. This time the inflation rate in Ireland is (1.3-1)/1 = 30% higher than the inflation rate in U.S. As we can see in the calculations we cannot tell about the exact inflation rates in two countries but we can understand which country has a relatively high or low inflation rate.
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