Assume that interest rate parity exists and will continue to exist. The U.S. interest rate was 4% while the Singapore interest rate was 5% at the beginning of the month. Assume the Singapore interest rate rises while the U.S. interest rate declines over the month. Based on this information, the forward rate of the Singapore dollar exhibited a at the beginning of the month, and _by the end of the month.

As per the interest rate parity theory (IRPT) , the difference between forward and spot rate of a currency is equal to the difference between their respective interest rates.

Forward rate for SGD i.e Singapore dollar means the US Dollars which can be purchased by 1 SGD i.e US Dollars per SGD.

Also, the currency whose interest rate is higher would be at a forward discount whereas the currency with lower interest rate would be at a forward premium. This effect mitigates the possibility of any arbitrage gain.

[tex]\frac{FR}{SR} = \frac{1\ +\ I_{USD} }{1\ +\ I_{SGD} }[/tex]

[tex]I_{USD}[/tex] = Interest rate in USA

[tex]I_{SGD}[/tex] = Interest rate in Singapore

As per the given information, FR = SR × [tex]\frac{(1\ +\ .04)}{(1\ +\ .05)}[/tex] = Spot Rate × 0.99

when interest rate in Singapore rises and falls in USA.. Let's assume, new interest rates being 3% in USA and 6% in Singapore.

Forward Rate would be, Spot Rate × [tex]\frac{(1\ +\ .03)}{(1\ +\ .06)}[/tex] = Spot rate × 0.972

Thus, it can be seen that SGD was at a forward discount at the beginning and with increase in it's interest rates and reduction in US Dollar interest rates, SGD forward discount increased.