How fast does an unpaid 18% credit card balance double?

Question

A credit card charges 18\% a year and you never pay it down. Solve in your head. Roughly how many years until the balance doubles? Aim: under 10 seconds.

Accepted Answer

Rule of 72, applied to debt: \frac{72}{18} = 4 	ext{ years.} Check: 1.18^{4} = 1.94, nearly a double. (The truth is \ln 2/\ln 1.18 \approx 4.2 years, so at this fairly high rate the rule runs a touch fast.) Takeaway. The same math that grows a nest egg grows a debt. At 18\% your balance doubles roughly every four years if untouched, which is why high-rate borrowing is so dangerous. Note the rule of 72 slightly overstates the speed once rates climb past the mid-teens.

How fast does an unpaid 18% credit card balance double?

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