The following rates currently exist:

Spot exchange rate: $1.000/euro.

Annual interest rate on 180-day euro-denominated bonds: 3%.

Annual interest rate on 180-day U.S. dollar-denominated bonds: 4%.

Investors currently expect the spot exchange rate to be about $1.005/euro in 180 days.

1. Show that uncovered interest parity holds (approximately) at these rates.

2. What is likely to be the effect on the spot exchange rate if the interest rate on 180-day dollar-denominated bonds declines to 3 percent? If the euro interest rate and the expected future spot rate are unchanged, and if uncovered interest parity is reestablished, what will the new current spot exchange rate be? Has the dollar appreciated or depreciated?

Please number each question with details and showing progress.