This thesis analyzes whether real interest rate differentials between Sweden and the United States affect the real USD/SEK exchange rate in the long run over the period 1987Q1 to 2024Q4. The analysis is conducted using the Engle-Granger two-step cointegration approach. First, unit root tests confirm that the real exchange rate and the interest rate differential are integrated of order one, I (1). However, the Augmented Dickey-Fuller test on the residuals indicates no evidence of cointegration, suggesting that there is no long-run equilibrium relationship between the two variables. The variables are tested for unit roots (ADF), multicollinearity, autocorrelation, heteroskedasticity, and serial correlation to ensure the robustness of the model. Given the absence of cointegration, the study shifts focus to the short run dynamics. The results show that real interest rate differentials have a statistically significant effect on short term fluctuations in the real USD/SEK exchange rate. In contrast, the real current account balances of both countries and dummy variables for the 2008 financial crisis and the COVID-19 pandemic do not have a significant impact. These findings suggest that while interest rate differentials matter in the short run, they do not determine the exchange rate in the long run.