The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

31. Cattarauqua Ginseng Enterprises, an American company, made a large sale to a Japanese importer. The total
    amount of the order was ¥25,000,000 (in Japanese yen), payable on September 24, 2006. Not wanting to gamble
    on movements in foreign exchange rates, on August 24 the company entered into a futures contract to exchange this
    amount into U.S. dollars on September 24.

a. Using the rates in the table from this section, what would the company receive in U.S. dollars?

b. Suppose that on September 24 the spot rate for Japanese yen was as listed below:

U.S. Dollar Equivalent Currency per U.S. Dollar

0.008588 116.4463

How much would the company have received if they had instead made their exchange on the spot market?

c. How much money did the company gain by making the futures exchange?

32. Some individuals and investment fi rms try to take advantage of the fl uctuations in foreign currency rates to make
    profi ts. This practice is sometimes called “forex trading” (“forex” being short for foreign exchange.) Suppose that such
    a trader is working with large enough amounts of money to be able to obtain the rates published in the Wall Street
    Journal. Determine the profi t (or loss) in U.S. dollars from each of these exchanges:

a. Bought $1,000,000 worth of euros at Wednesday’s closing price and converted back to U.S. dollars at Thursday’s.

b. Bought $2,000,000 worth of Colombian pesos at Wednesday’s price and converted back to U.S. dollars at Thursday’s

c. Converted $1,600,000 into Singapore dollars at Wednesday’s rate and back to U.S. dollars at Thursday’s

33. A sign posted in the snack bar of a tennis club in Hamilton, Ontario, says “15% exchange on U.S. funds. Change given
    in Canadian funds only.” Kevin’s lunch cost C$8.43 and he paid with a US$10 bill. How much change did he get?


34. Andrew and his sister Alison both opened investment accounts on May 13, 1992. Andrew deposited $3,500 when he
    opened the account, and made no other deposits or withdrawals. His account has earned 4.8% interest compounded
    monthly.
    Allison made a deposit of $3,500, also on May 13, 1992, and also made no additional contributions to or withdrawals
    from her account. However, Allison was living in Canada at the time, and opened her account at a Canadian bank.
    Therefore, Allison fi rst converted her US$3,500 into Canadian dollars, and then deposited the resulting Canadian
    money into the account. Her account has also earned 4.8% interest compounded monthly.
    The U.S.-Canadian exchange rates are given below:

Date U.S. Dollar Equivalent Currency per U.S. Dollar

On May 13, 1992 0.8314 1.2028

On May 13, 2002 0.6429 1.5555

a. What was the value of Andrew’s account on May 13, 2002?

b. What was the value, in U.S. dollars, of Allison’s account on May 13, 2002?

c. Both Allison and Andrew contributed the same amount of money to their accounts, both earned the same

compound interest rate, and both had their money on deposit for the same amount of time. Who came out ahead,

as measured in U.S. dollars? Why didn’t they both have the same amount?

Exercises 11.1 483