Assume that Social Security promises you $$40,000$ per year starting when you retire $45$ years from today $($the first $$40,000$ will be paid $45$ years from now$).$ If your discount rate is $7\%,$ compounded annually, and you plan to live for $15$ years after retiring $($so that you will receive a total of $16$ payments including the first one$),$ what is the value today of Social Security's promise?

The value today of Social Security's promise is $ $($Round to the nearest cent$)$