Gold or Bills

This is from Sanjoy Mahajan’s The Art of Insight Problem 1.4

As a bank robber sitting in the vault planning your getaway, do you fill your suitcase with gold bars or $100 bills? Assume first that how much you can carry is a fixed weight. Then redo your analysis assuming that how much you can carry is a fixed volume.

As I estimated in suitcase of money the mass of a paper note is about 1 gram, and the volume is about 1 cm³. So the mass density of an $100 note is $100 per gram, and the volume density is $100 per cubic centimetre.

As I estimated in Value of Gold the volume density of gold is about $2000 per cubic centimetre. So clearly for a fixed volume you are much better off filling a suitcase with gold bars.

However gold is quite dense, with a density of about 20 grams per cubic centimetre (about twice the “typical” amount of 10 grams per cubic centimetre for many metals). So the mass density is about $100 per gram, similar to a money note. I actually overestimated the value density slightly, so in fact for a fixed weight you would be better off with paper money.

Note that a small suitcase of money weighs around 50 kilograms. Gold is about 20 times denser, so would weigh 1 tonne. In practice weight is more likely to be the limiting factor and you’re better off with a suitcase full of money.