Answer to Question #224647 in Financial Math for Collins

Question

Cal Bank believes the US dollar will appreciate over the next five days from GHS 4.48 to GHS 4.50. The following annual interest rates apply:
Currency. Lending Rate Borrowing Rate
Dollars 7.10% 7.50%
Ghana Cedis 6.80% 7.25%

Cal Bank has the capacity to borrow either GHS 10 million or $5 million. If Cal Bank's forecast is correct, what will its dollar profit be from speculation over the five-days period (assuming it does not use any of its existing consumer deposits to capitalize on its expectations)?

Answer 1

The speculative profit can be made in the following way :

i) Borrow GHS 10million for 5 days at 7.25% , Amount to be repaid after 5 days = GHS 10 million $\times$ (1+0.0725$\times$ $\frac{5}{365}$ ) = GHS 10,009,932

ii) Convert the GHS 10 million to Dollars to get $\frac{10million}{4.48}$ = $\$$ 2,232,142.86

iii) Invest this amount for 5 days at 7.10% to get $ 2232142.86 $\times$ (1+0.071$\times$ $\frac{5}{365}$ ) = $\$$ 2,234,313.85 after 5 days

iv) After 5 days, get $2,234,313.85 and sell it at 4.50 (if speculation is correct) to get GHS 2234313.85$\times$ 4.50 = GHS 10,054,412

v) Repay the GHS borrowing amount of GHS 10,009,932

and make a speculative profit of GHS 10,054,412 - GHS 10,009,932 = GHS 44481

Profit in Dollars = GHS 44481$/$ 4.50 = $9884.62