Question

The three-month dollar interest rate in New York is 3.80% per annum. Alternatively, the three-month euro interest rate in Frankfort is 5.40% p.a. The current $/€ spot exchange rate is $1.1220/€. The euro three-month forward rate is quoted at $1.1210/€.

2. Use the International Fisher Effect (IFE) to find what should be the expected three-month spot exchange rate of dollars against the euro (If not performing chain calculations, use interest rates up to four decimal places, and again use the proper relationship that describes IFE).   Answer suppose to be $1.1176/€

3. Assume that the real rate of interest in both the euro zone and the U.S. is 1.96% per annum; use the Fisher Effect (FE) to calculate the expected annualized three-month rates of inflation in the euro zone and the U.S. (Expressed as a % p.a. up to four decimal places).   

4. Use the results in question 4 above and the Relative Purchasing Power Parity (RPPP) relationship to estimate the expected three-month spot exchange rate of the dollars against the euro. Answer suppose to be $1.1176/€

5. What do you notice about the answers to questions 2,3, and 5? Are they what you expect?

I need to know how to get those answer. Thank you! Show me in detail. You can skip part 5 if you want to.

Answer 1

Given

Interest rate of dollar, i_{​​​​​​d} = 3.80% per annum = 0.95% for 3 months

Interest rate of euro, i_{​​​​​​e} = 5.40% per annum = 1.35% for 3 months

Spot rate, SR = $1.1220/€

3 months forward rate = $1.1210/€

1) Expected 3 months exchange rate using International Fisher Effect

= SR(1+i_{​​​​​​d} )/(1+i_{​​​​​​e} )

= 1.1220(1.0095)/1.0135

= $ 1.1176/€

2) If the real interest rate of both country is 1.96% per annum, the inflation rate can be calculated using the formula

(1+ Nominal rate) = (1+Real rate) (1+Inflation rate)

Inflation rate = [(1+Nominal rate)/(1+Real rate)] - 1

3 months inflation rate of dollar

= (1.0095/1.0049) -1

= 0.00457

= 0.46% or 1.83% per annum

3 months inflation rate of euro

= (1.0135/1.0049) -1

= 0.00856

= 0.86% or 3.42% per annum

3) Expected 3 months exchange rate using Relative Purchasing Power Parity

= SR(1+ Inflation rate_dollar )/(1+ Inflation rate _euro)

= 1.1220(1.0046)/(1.0086)

= $ 1.1176/€