Why do banks charge a significantly lesser rate for a 15 yr. fixed mortgage than a 30yr. (though they know it will not earn them the same amount of money)?
A simplistic model of where banks get the money to lend to borrowers is that they "borrow" money from investors that want to earn a return on the money that they provide. The actual mechanics of that process are much more complicated, but the gist is that if those investors want to tie their money up for a longer period, they expect to get a higher return, thus 30-year mortgages require a higher interest rate than 15-year mortgages. In addition, the "usual" consensus in the market is that interest rates will rise in the future, so interest rates for longer-term loans are higher
While it's true that the bank gets "more money" overall from a higher-rate mortgage, the fact that that additional money doesn't come until several years into the loan (and that money loses value over time due to inflation) makes a lower-rate 15 year mortgage roughly equivalent to a higher-rate 30-year mortgage.