Answer to Question #221866 in Finance for ycw

Question

1. Suppose 90-day investments in Europe have a 5% annualized return. In the United States, 90-day investments of similar risk have a 7% annualized return. In today’s 90-day forward market, €1 equals $1.32. If interest rate parity holds, what is the spot exchange rate ($/€)?

Answer 1

Calculation of Expected 3 months spot rate for euro in US dollars

Interest rate in US (rd)(90 days) = $\frac{7}{4}$% = 1.75% P.Q(90 days)

Interest rate in Europe (rf)(90 days) =$\frac{5}{4}$% = 1.25% P.Q(90 days)

Forward rate(f) $1.32 = €1

to find out the spot rate, we use Interest rate parity theorem(IRPT) ,the formula for IRPT is,

IRPT$= \frac{1+rd}{1+rf}=\frac{F}{S}$,

where, F is the forward foreign exchange rate,

S is the spot exchange rate,

(rd) is interest rate in domestic currency

and (rf) is the interest rate in foreign currency

IRPT$=\frac{1+0.0175}{1+0.0125}=\frac{1.32}{S}$

IRPT$=\frac{1.0175}{1.0125}=\frac{1.32}{S}$

IPRT$= S =\frac{1.32\times1.0125}{1.0175}$

IPRT$=S=1.3135$

the spot exchange rate ($/€) S = 1.3135