Explanation

To solve this problem, we need to use two key formulas:

1. Real Interest Rate Formula

$R_{\text{real}} = \frac{1 + R_{\text{nom}}}{1 + R_{\text{infl}}} - 1$

2. Covered Interest Parity Formula

$F = S \cdot \frac{(1 + R_{\text{CAD}})^t}{(1 + R_{\text{USD}})^t}$

Given:

• Spot rate (S) = CAD 1.21 per USD 1
• Forward rate (F) = CAD 1.19 per USD 1
• US risk-free rate (R_USD) = 0.85% = 0.0085
• US inflation (R_infl, USD) = 2.50% = 0.025
• Canada inflation (R_infl, CAD) = 2.80% = 0.028

Step 1: Calculate Canadian nominal interest rate using CIP $(1 + R_{\text{CAD}})^1 = F \cdot \frac{(1 + R_{\text{USD}})}{S}$ $(1 + R_{\text{CAD}}) = 1.19 \cdot \frac{(1 + 0.0085)}{1.21}$ $(1 + R_{\text{CAD}}) = 1.19 \cdot \frac{1.0085}{1.21}$ $(1 + R_{\text{CAD}}) = 1.19 \cdot 0.8339$ $(1 + R_{\text{CAD}}) = 0.9918$ $R_{\text{CAD}} = 0.9918 - 1 = -0.00817 = -0.817\%$

Step 2: Calculate real interest rates

US Real Interest Rate: $R_{\text{USD, real}} = \frac{1 + 0.0085}{1 + 0.025} - 1$ $R_{\text{USD, real}} = \frac{1.0085}{1.025} - 1$ $R_{\text{USD, real}} = 0.9839 - 1 = -0.0161 = -1.61\%$

Canada Real Interest Rate: $R_{\text{CAD, real}} = \frac{1 + (-0.00817)}{1 + 0.028} - 1$ $R_{\text{CAD, real}} = \frac{0.99183}{1.028} - 1$ $R_{\text{CAD, real}} = 0.9648 - 1 = -0.0352 = -3.52\%$

Step 3: Calculate the difference $\text{Difference} = |R_{\text{USD, real}} - R_{\text{CAD, real}}|$ $\text{Difference} = |-1.61\% - (-3.52\%)|$ $\text{Difference} = |1.91\%| = 1.91\%$

Therefore, the best estimate of the difference between the real interest rates in Canada and the US is 1.91%.