In the spring of 2010, Afghan officials struck a deal to free an Afghan diplomat held hostage by Al Qaeda. But the price was steep - $5 million. To come up with the money, [senior security officials] turned to a secret fund that the Central Intelligence Agency bankrolled with monthly cash deliveries to the presidential palace in Kabul, according to several Afghan officials. The Afghan government, they said, had already squirreled away about $1 million from that fund. Within weeks, that money ... was handed over to Al Qaeda, replenishing its coffers after a relentless C.I.A. campaign of drone strikes in Pakistan had decimated the militant network's upper ranks. The C.I.A.'s contribution to Qaeda's bottom line, though, was no well-laid trap. It was just another in a long list of examples of how the United States, largely because of poor oversight and loose financial controls, has sometimes inadvertently financed the very militants it is fighting. While refusing to pay ransoms for Americans kidnapped by Al Qaeda, the Taliban or, more recently, the Islamic State, the United States has spent hundreds of billions of dollars over the last decade at war in Iraq and Afghanistan, some of which has been siphoned off to enemy fighters. The C.I.A., meanwhile, continued dropping off bags of cash - ranging each time from a few hundred thousand dollars to more than $1 million - at the presidential palace every month until last year, when Mr. Karzai stepped down. The money was used to buy the loyalty of warlords, legislators and other prominent - and potentially troublesome - Afghans, helping the palace finance a vast patronage network that secured Mr. Karzai's power base.