Final answer:
The US dollar should depreciate by approximately 3.96% against the Japanese yen over a year due to a 5% inflation rate in the US and a 1% rate in Japan, under relative PPP. The interest rate differential is expected to be approximately 4%, corresponding to the inflation rate differential between the two countries.
Step-by-step explanation:
If the US inflation rate is 5% over one year but the inflation rate in Japan is only 1%, according to relative Purchasing Power Parity (PPP), the US dollar should depreciate against the Japanese yen. Relative PPP implies that the exchange rate should adjust to offset the inflation differential between two countries. On the assumption that PPP holds, the percent change in the exchange rate should be approximately equal to the inflation differential.
Using the formula:
E1 = E0 * (1+inflation home) / (1+inflation foreign),
where E0 is the current exchange rate and E1 is the future exchange rate, we can predict the change. Assuming an exchange rate of 100 yen/dollar (E0) for easy calculation, the expected exchange rate (E1) in one year would be:
100 * (1+0.05) / (1+0.01) = 100 * 1.05 / 1.01 = 103.96 yen/dollar. This indicates the US dollar would depreciate to 103.96 yen per dollar and implies a depreciation rate of about 3.96%.
The relative interest rate differential between the two countries would be expected to reflect the inflation differential. Given that the US inflation rate is higher by 4% (5% - 1%), interest rates in the US would be higher than those in Japan by approximately 4%, assuming that other factors remain constant and the Fisher Effect applies, which states that the nominal interest rate is approximately equal to the real interest rate plus the expected inflation rate.