Maxwell Corporation has a customer who wants to purchase $$50,000$ of goods on credit. Maxwell estimates that the customer has a $97\%$ probability of paying the $$50,000$ in four months and a $3\%$ probability of a complete default $($paying no cash at all$).$ Assume an investment of $85\%$ of the amount, made at the time of the sale, and a required return of $10\%$ APY. What is the indifference payment probability $($p$*)?$