Problem:

Jessica is in the market for a new car. She has narrowed her search down to 2 models. Model A costs $24,000 and Model B costs $18,000. With both cars she plans to pay cash and own them for 3 years before trading in for a new car. Her research indicates that the trade in value for Model A after 3 years is 50% of the initial purchase price, while the trade in value for Model B is 25%. Jessica has no emotional attachment to either model and wants to make a strictly financial decision. The interest rate is 6%. For simplicity assume that operating and maintenance costs for the models are identical every year. Which model is the better decision and how much "cheaper" is it than the alternative?

Explain comprehensively and provide step by step solution.