American Dream : calcul de salaire et coût de la vie

An immigrant arrives in the US with an initial salary of $S_i = 20,000$ dollars. They aim for the American Dream, defined here as tripling their initial salary to reach a target salary $S_t$. However, the city they live in has a cost of living index of $C_L = 1.2$. To maintain the actual purchasing power of the target salary $S_t$, one must calculate the adjusted salary $S_a$, where $S_a = S_t \times C_L$.

1. Calculate the target salary $S_t$ using the factor of $3$.
2. Determine the adjusted salary $S_a$ needed to face the cost of living $C_L = 1.2$.
3. Write a short paragraph in English explaining why the cost of living index makes the 'American Dream' more difficult to achieve, using the calculated values.