A family is considering getting a loan to purchase a new home. Below is a payoff table that lists four mortgage options are available and the payoff table for the outcomes is shown below. The payoffs represent total interest paid under three future interest rate situations Outcome Probability 0.52 0.33 0.15 Decision Rates Rise Rates Stable Rates Fall 1-year ARM $66,645 $43,650 $38,560 3-year ARM $62,1 $47.0 $42,0 5-year ARM $55,895 $50,894 $48,134 30-year fixed $52,276 $52.276 $52,276 The probability of rates rising is 0.52 rates stable is 0.33, and rates falling is 0.15 What is the expected payoff for the 3-year ARM