Take a penny, double it, double it, double it ... How Long Before National Debt Is Paid?

If you take the national debt as $13 trillion (approximate as of June 10), and you received one penny on day one and had it double every day after, it would take 51 days to have enough pennies to pay off the national debt. And every penny minted after 1982 weighs about 2.5 grams, so that many pennies would weigh 3.25 quadrillion grams, which is about 3.6 billion tons!

You can figure this out using some fairly simple mathematical formulas. On day one, you receive one penny, on day two, two pennies, on day three, four pennies, and so on. You can summarize this as receiving the initial amount of pennies (I) which is one, times 2 multiplied by itself the number of days it has been doubled (D) times. Using the formula I*2^(D-1), you get 2^(D-1). On day one, that's 2^0=1, day two is 2^1=2, and so on. Since the number of pennies you receive is cumulative, not replaced every day, you must add the days together, and figure out when the total is greater than 13 trillion, not just one day.

The easiest way to do this to figure out on which day you would receive enough pennies to pay off the entire national debt with the pennies from that day alone, and the day before that is when you would receive enough pennies to pay off the debt cumulatively. To figure out which day you would receive enough pennies to pay off the debt singularly, use the formula 2^(D-1) and set it equal to the number of pennies you need. 2^(D-1)=1,300,000,000,000,000 (1.3 quadrillion pennies!). Solving for D says that D=51.3, approximately. So rounding up, on day 52 you would receive enough pennies to pay off the national debt. That means that adding all the pennies up from previous days, on day 51 you would have enough pennies to pay off the debt.