Question

An investor starts with $1 million and converts it to 0.75 million pounds, which is then invested for one year. In a year the investor has 0.7795 million pounds, which she then converts to dollars at an exchange rate of 0.72 pounds per dollar. The U.S. dollar annual rate of return earned was _____.

Answer 1

Multiple choices are:

4.97%

5.27%

6.45%

7.69%

8.26%

The U.S. dollar annual rate of return earned was is 8.26%

Step-by-step explanation:

Initial investment =$1 million

dollar value of investment after 1 year=pounds value*$1/pounds exchange rate

pounds value of investment after 1 year=0.7795 million pounds

$1 equals to 0.72 pounds in year

dollar value of investment after 1 year=0.7795*$1/0.72

dollar value of investment after 1 year=$1.082638889

U.S dollar annual rate of return earned=dollar value of investment after 1 year-initial dollar investment/initial dollar investment

U.S dollar annual rate of return earned=($1.082638889 million-$1 million)/$1 million*100

U.S dollar annual rate of return earned=0.082638889

U.S dollar annual rate of return earned=8.26%

Answer 2

8.26%

Step-by-step explanation:

If the investor had, at the end of the year, 0.7795 million pounds, when converting that amount to U.S. dollars at an exchange rate of 0.72 pounds per dollar, the investor would have:

`A = 0.7795\ million\ pounds*(\$1)/(0.72\ pounds)\\A=\$1.08264\ million`

Since the investment lasted for exactly 1 year, the annual rate of return was:

`r=(\$1.08264)/(\$1)-1\\ r=0.08264\\r=8.26\%`

The U.S. dollar annual rate of return earned was 8.26%.