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## Q. 4.ST.3

Smart Banking Corp. can borrow \$5 million at 6 per cent annualized. It can use the proceeds to invest in Canadian dollars at 9 percent annualized over a six-day period. The Canadian dollar is worth \$.95 and is expected to be worth \$.94 in six days. Based on this information, should Smart Banking Corp. borrow U.S. dollars and invest in Canadian
dollars? What would be the gain or loss in U.S. dollars?

## Verified Solution

Smart Banking Corp. should not pursue the strategy because a loss would result, as shown here.
a. Borrow \$5 million.
b. Convert \$5 million to C\$5,263,158 (based on the spot exchange rate of \$.95 per C\$).
c. Invest the C\$ at 9 percent annualized, which represents a return of .15 percent over 6 days, so the C\$ received after 6 days = C\$5,271,053 (computed as C\$5,263,158 × [1 + .0015]).
d. Convert the C\$ received back to U.S. dollars after 6 days: C\$5,271,053 = \$4,954,789 (based on anticipated exchange rate of \$.94 per C\$ after 6 days).
e. The interest rate owed on the U.S. dollar loan is .10 percent over the 6-day period. Thus, the amount owed as a result of the loan is \$5,005,000 [computed
as \$5,000,000 × (1 + .001)].
f. The strategy is expected to cause a gain of \$4,954,789 – \$5,005,000 = -\$50,211.