Your engineers are developing a new product to launch next year that will require both software and hardware innovations. The software team requests a budget of $$5$ million and forecasts a $70\%$ chance of success. The hardware team requests a $$10$ million budget and forecasts a $30\%$ chance of success. Both teams will need $6$ months to work on the product, and the risk$-$free interest rate is $4\%$ APR with semiannual compounding.