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Theory of Purchasing Power Parity: Exchange and Interest Rates

Congratulations, you just won the Irish Lottery! You bought a ticket while you were on vacation in Ireland, and you just won a 1 million Euro jackpot after all taxes were taken out.

1. If the current exchange rate is US$1 equals 1.25 Euros, how much did you win in US dollars?
2. 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? If you had taken your winnings back to the USA, how many dollars would you have?
3. 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? Did you do better off leaving your winnings in Ireland or bringing them home to the USA?
4. Explain how banks and individuals can use "covered interest arbitrage" to protect themselves when they make international financial investments.
5. Using the theory of purchasing power parity, explain how inflation impacts exchange rates. 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?

Solution Preview

Congratulations, you just won the Irish Lottery! You bought a ticket while you were on vacation in Ireland, and you just won a 1 million Euro jackpot after all taxes were taken out. If the current exchange rate is US $1 equals 1.25 Euros, how much did you win in US dollars?
Show all calculations

In US dollars = Euro * Exchange rate factor
= 1million *.8
=US$ 800000

Note:
Exchange rate factor for Euro
1Euro = 1/1.25 US$
=.8 mnUS$

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? If you had taken you winnings back to the USA, how many dollars would you have?

Show all calculations
Amount= Present value *(1+r)^n
Where r= interest rate, n= duration
If you left your winnings in Ireland, how many Euros would you have in a year?
Amount in Euros= 1000000*(1+.05)^1
=Euro1050000
If you had taken you winnings back to the USA, how many dollars would you have?
Amount in US$= 800000*(1+.02)^1
=US$ 816000

Suppose when you cashed in your CD in ...

Solution Summary

This solution provides calculations for the exchange rate and present value and provides an explanation for covered interest arbitrage and the theory of purchasing power parity to explain inflation's impact on interest rates.

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