Question

Suppose that on January 1, the cost of borrowing French francs for the year is 18%. During the year, U.S. inflation is 5%, and French inflation is 9%. At the same time, the exchange rate changes from FF 1 = $0.15 on January 1 to FF 1 = $0.10 on December 31. What was the real U.S. dollar cost of borrowing francs (real interest rate in U.S.) for the year?

Answer 1

-25.08%.

Step-by-step explanation:

Given that, during the year, the franc devalued by (0.15 - 0.10)/0.15 = 33.33%.

Then, the nominal dollar cost of borrowing French francs, therefore, was 0.18(1 - 0.3333) - 0.3333 = -21.33%.

Thus, for each dollar's worth of francs borrowed on January 1, it cost only $1 - $0.2133 = $0.7867 to repay the principal plus interest.

Also, with U.S. inflation of 5% during the year, the real dollar cost of repaying the principal and interest is $0.7867/1.05 = $0.7492.

Subtracting the original $1 borrowed, it shows that the real dollar cost of repaying the franc loan is -$0.2508 or a real dollar interest rate of -25.08%.