Suppose that you expect during the next year the dollar will appreciate against the pound from 0.5 pound to the dollar to 0.75 pound to the dollar. How much will you expect to make on an investment of $10,000 in British government securities that will mature in one year and pay interest of 8%?

Question

Quizplus · Accepted Answer

First, we need to calculate how much the investment is worth in pounds when we make it. Since the exchange rate is 0.5 pound to the dollar, $10,000 is worth 5,000 pounds.

Next, we calculate the interest earned on the investment in pounds, which is 8% of 5,000 pounds, or 400 pounds.

Finally, we need to convert the investment and interest earned back into dollars using the new exchange rate of 0.75 pound to the dollar. The investment is now worth 5,000 pounds * 0.75 pound/dollar = $3,750. The interest earned is worth 400 pounds * 0.75 pound/dollar = $300.

The total value of the investment at maturity is $4,050 ($3,750 + $300). This represents a return of 4.5% ($4,050 / $10,000). However, since we expect the dollar to appreciate against the pound, the return in dollars will be lower than 4.5%.

To calculate the expected return in dollars, we take the difference between the old and new exchange rates, and divide by the old exchange rate:

(0.75 - 0.5) / 0.5 = 0.5, or 50%.

So we expect the dollar to appreciate by 50% against the pound. Therefore, the expected return on our investment in dollars is 4.5% minus 50%, or -45.5%.

However, the question is asking for the expected profit, not the expected return. To calculate this, we take the total value of the investment at maturity and subtract the initial investment:

$4,050 - $10,000 = -$5,950

This represents a loss of $5,950 on the investment, or -59.5% of the initial investment.

Therefore, the correct answer is B, -59.5%.

Suppose That You Expect During the Next Year the Dollar