Suppose the (riskless) rate on Euro-denominated T-bills is lower than the U.S. T

Question

Suppose the (riskless) rate on Euro-denominated T-bills is lower than the U.S. Treasury bill rate. If the spot rate S is quoted $ per Euro, would you expect that the forward rate F (also $/Euro) will be higher or lower than S? Explain. Does this indicate whether the Euro will rise or decline in value in the future? Explain. * Note: This is the second time i post the question because first time someone answered it as if i say Euro-denominated is "higher" than US treasury bill..... the question as you see said "lower"

Explanation / Answer

As per the Interest rate Parity theory, the differential between the spot and forward rate is equal to the differential in interest rates of two countries. It usually means that the lower the interest rate of a particular country, the higher the forward rate will be. This can be explained better with an example, using the question you described.

Country A and B's functional currency is the Euro and USD respectively.
The A/B forward rate is 1.25, i.e, $1.25 per Euro
Interest rate in A is 5%. B is 6%
Now to calculate the forward rate.
As per the IRP formula, Forward rate = spot rate * (1+int rate of variable ccy)/(int rate of base ccy)
Here B is variable and A is the base.
FR = 1.25 * (1+0.06)/(1+0.05)
= 1.25 * 1.06/1.05
= 1.2619

Here the forward rate has increased, which means, that more units of USD will have to be spent to purchase 1 Euro. Essentially what has happened is that due to higher interest rates in Country B as compared to Country A, the forward rate estimate is showing a depreciated USD and an appreciated Euro.

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