To answer the question on how interest rates affect foreign exchange rates, you should first refresh yourself on what a foreign exchange rate is. It’s always a combination of two currencies (e.g. USD/AUD or EURO/USD).
Changes in domestic interest rates in one of the countries affect the foreign exchange rate as the demand for the currency that has had a change of interest rate will change.
Let’s take the example of the USD/AUD. Assume that U.S interest rates are 2% and Australian interest rates are 5%. An increase in U.S official interest rates by 0.25 basis points would take the official rate to 2.25%. Assume that Australian interest rates, and hence the demand for the AUD, remain constant. The increase in the U.S rate would entice some people to move their investments (e.g. shares, property or other currency holdings) to hold U.S currency, because they would get paid a higher interest rate following the change. Even though U.S interest rates are relatively low in the example above, the marginal change in consumer behaviour will cause an increase in demand for the USD and hence and increase in the USD/AUD foreign exchange rate.
Clearly an increase in the US official rate, holding all other interest rates constant, would not only affect the USD/AUD rate. In fact, all foreign exchange rates where the USD is listed first (USD/x) should increase.
It should be clear from the above example that if the opposite were to happen, interest rates in the U.S reduced by 0.25 basis points to 1.75%, then the demand for the USD would decrease as investors move out of holding USD and into other investments (shares, property or other currencies). This decrease in the demand for holding the USD will lead to a fall in all foreign exchange rates where the USD is listed first (USD/x).
An increase in a domestic interest rate, holding all else constant, will increase demand for that country’s currency causing an appreciation of any exchange rates where the currency that has had the increase in demand is listed first.
A decrease in a domestic interest rate, holding all else constant, will decrease demand for that country’s currency causing a depreciation of any exchange rates where the currency that has had the decrease in demand is listed first.