Currency Question

Why wouldn’t the return be as follows? covert $100 to 66.67 pounds. Invest at 12% and have 74.67 pounds at end of year. Convert to $119.47 for a 19.47% return? A U.S. investor purchased a U.K. bond one year ago. The exchange rate at the time was 1.5 to 1 (dollars to pounds) and the beginning-of-period ratio of the price levels of the consumption baskets was 2 to 1 (dollars to pounds). Beginning of the year interest rates were 7% in the U.S. and 12% in the U.K. Inflation during the year was expected to be 5% in the U.S. and 10% in the U.K. Today the exchange rate is 1.6. What is the ex-post domestic currency return on the U.K. bond to the U.S. investor? A) 14.67%. B) 5.33%. C) 18.67%. The correct answer was C) 18.67%. The dollar was expected to appreciate (lower inflation), but depreciated by 6.67% (= 1.6 / 1.5 = 1.0667 or 6.67%) instead. Hence, the return to U.S. investor is the foreign interest rate plus currency appreciation, or 18.67% (= 12% foreign rate + 6.67% appreciation).

that is correct as well. u answered with exact methodology. the answer given is just a linear approximation.