I was working on a practice test for Level 1 when I came across this bugger. The answer provided makes absolutely no sense to me. I honestly think they made an error. If I don’t get to the bottom of this it will really bother me. Please give it a shot and let me know. Should be very simple.

Question:

An investor examines the following rate quotes for the Brazilian real and the Australian dollar and shorts BRL 500,000.

Spot rate BRL/AUD 2.1128 BRL 1-year interest rate 4.1% ----------------------------------------------------------------------------------------- Forward rate BRL/AUD 2.1388 AUD 1-year interest rate 3.1%

Question: The risk-free arbitrage profit that is available is closest to:

a) BRL6,405. b) BRL1,344. c) -BRL6,327

b) is the Correct answer…somehow

This is how I got my answer: Scenario 1(invest locally) vs Scenario 2(invest abroad then convert back):

Scenario 1.

Step 1: Simply invest 500,000 BRL locally @ 4.1% = 500,000 * 1.041 = 520,500 BRL

VS.

Scenario 2.

Step 1: Convert 500,000 BRL to AUD, @ BRL/AUD = 2.1128 (2.1128 AUD for every 1 BRL) 500,000 * 2.1128 = 1,056,400 AUD

Step 2: Invest that 1,056,400 AUD @ 3.1% for 1 year 1,056,400 * 1.031 = 1,089,148 AUD

Step 3: Convert that 1,089,148 AUD back to BRL @ BRL/AUD 2.1388 (Locked in Forward Rate) 2.1388 AUD for every 1 BRL, so 1,089,148/2.1388 = 509,233 BRL

RESULT: Scenario 2 - Scenario 1 Arbitrage Profit = 509,233 BR - 520,500 BRL = -11,267 BRL Ergo, no arbitrage profit, you are better off keeping those BRL and investing locally Am I missing something here?? or is it an error?

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This is what the answer key gave me:

Left side of equation: BRL500,000 x (1+.041) = BRL520,500

Right Side:

1

BRL500,000 x (1/2.1128AUD/BRL) = AUD236,653 **500,000 BRL= 1,056,400 AUD not 236,653 AUD wtf?** Convert domestic to foreign

2

AUD236,653 x (1.031) = AUD243,989

Invest foreign @ foreign rate

3

AUD243,989 x 2.1388 = BRL521,844

Convert foreign to domestic

Arbitrage profit = BRL521,844 - BRL520,500= BRL1,344

Thanks in advance!