The 6-month interest rate on 180-day U.S. Treasury bills is 7.64%. In the foreign exchange markets, the spot rate between U.S. dollars and British pounds is 1 pound = $1.5525. The 180-day (6-month) forward rate is 1 pound = $1.5188. Determine the expected rate of interest on 6-month British government debt securities, assuming interest rate parity between the dollar and pound exists.

Question

Quizplus · Accepted Answer

Interest rate parity (IRP) implies that the difference in interest rates between two countries is equal to the difference between the forward and spot exchange rates. The formula to calculate the expected foreign interest rate (i_f) given the domestic interest rate (i_d), the spot exchange rate (S), and the forward exchange rate (F) is:$$i_f = i_d + \left( \frac{F - S}{S} \right) \times 100$$Given:- $i_d = 7.64\%$- $S = 1.5525$ (spot rate, $/pound)- $F = 1.5188$ (forward rate, $/pound)Plugging the values into the formula:$$i_f = 7.64\% + \left( \frac{1.5188 - 1.5525}{1.5525} \right) \times 100$$$$i_f = 7.64\% - 2.17\%$$$$i_f = 5.47\%$$However, the correct calculation should actually be:$$i_f = 7.64\% + \left( \frac{1.5525 - 1.5188}{1.5188} \right) \times 100$$$$i_f = 7.64\% + \left( \frac{0.0337}{1.5188} \right) \times 100$$$$i_f = 7.64\% + 2.22\%$$$$i_f = 9.86\%$$The calculation provided was incorrect, leading to an incorrect conclusion. The correct approach to find the expected rate of interest on 6-month British government debt securities, assuming interest rate parity, involves correctly applying the formula and accurately calculating the percentage change between the forward and spot rates, then adjusting the domestic interest rate accordingly. The mistake was in the arithmetic and the interpretation of the formula, leading to an incorrect answer choice. Given the options provided and the correct approach to the calculation, none of the options accurately reflect the corrected calculation. The closest provided option to the correct calculation is 10.03%, but the explanation led to an incorrect justification for choosing 5.47%. The correct answer should reflect the principles of interest rate parity and the accurate calculation based on the given forward and spot rates, which was not properly executed in the explanation.

The 6-Month Interest Rate on 180-Day U