President Barack Obama’s vow that the United States would “hunt down” Islamic State terrorists “wherever they are” could cost the government $100 million a week or more if airstrikes are extended into Syria, experts told NBC News.

The fight against ISIS will in some ways be similar to the campaign against terrorist group al-Qaeda — both are nebulous organizations whose members are not from one particular country and both have sympathizers all over the globe.

Obama said that 475 military personnel would be deployed to Iraq over the next week, yet he also said that he doesn’t want to put American “boots on the ground” in Syria, where ISIS is based, so it’s unclear what exact resources will go into the fight.

“The current cost of ongoing activities in Iraq varies but is about $7.5 million per day based upon a snapshot of operations that have occurred as of Aug. 26,” Pentagon spokeswoman Cmdr. Elissa Smith told NBC News on Thursday. “These include the DoD mission and personnel costs in Iraq to include air operations, and associated enablers such as logistics and intelligence, surveillance and reconnaissance support.”

At that rate, a year of operations would cost $2.7 billion, but the Iraq operations have been relatively light. An accelerated mission to hunt down ISIS — “to the gates of hell,” as Vice President Joe Biden put it — could come with a significantly higher price tag.

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"The big unknown, though, is how long does this go on"

It was estimated that in 2014, it costs an average of $2.1 million a year for every American troop serving in Afghanistan, according to a report from the Center for Strategic and Budgetary Assessments. The author of that study, CSBA Senior Fellow Todd Harrison, told NBC News on Thursday that he guessed costs for the war against ISIS could start low and balloon.

“I think a figure of 50 million a week, which is in line with what the Pentagon is saying, is a good starting point for estimating what our air operations will be,” Harrison said. “I would expect in the next couple of weeks as we possibly expand this into Syria those flights would increase, so we would see the burn rate increase. It could get up to 100, maybe 200 million a week.”

That would put the yearly cost at $5 to $10 billion.

“It sounds like a lot of money, but in the defense budget that’s a round-off error,” Harrison said. The Defense Department budget for fiscal year 2014 authorized over $550 billion in spending on national defense, with an additional $80 billion for what’s called “Overseas Contingency Operations,” or OCO. That OCO fund is where officials have said funds for the ISIS fight will come from.

Harrison said that some comparisons could be made to the operations in Libya to oust Muammar Gaddafi in 2011, where after some of the major targets were taken out, the fight became more of a slog. Libya is on the verge of being a completely failed state today.

“The big unknown, though, is how long does this go on, and what are we doing on the ground at the same time,” Harrison said. “If we’re running at a cost of maybe 100 or 200 million week, if that persists for a long time, then you are talking a lot of money.”

"Nations notoriously underestimate what wars will cost going in"

Gordon Adams, former Associate Director for National Security and International Affairs at the Office of Management and Budget in the Clinton administration, and currently a professor in the School of International Service at American University, said the campaign against ISIS would involve five elements: the air operation in Iraq, extending airstrikes into Syria, military assistance to Iraqi and Kurdish forces, providing military help for moderate Syrian forces, and paying other countries for their support.

Using a “back of the envelope” calculation based on those elements, Professor Adams estimated a cost of about $15-$20 billion a year. Adams predicted that only Jordan and perhaps some of the less-wealthy NATO countries would want financial help from the U.S. if they joined the coalition.

Brown University’s CostsofWar.org project has estimated that the war in Iraq has cost the United States $2.2 trillion since 2001, excluding future interest on the war’s debt. And Professor Catherine Lutz, with the school’s Watson Institute for International Studies, notes that there will likely be untold costs that cannot be measured, including hostility to the U.S. and increased refugee numbers.

“Nations notoriously underestimate what wars will cost going in — the U.S. has been no different in these last two wars."