This is from Sanjoy Mahajan's The Art of Insight Problem 1.3

In the movies, and perhaps in reality, cocaine and elections are bought with a suitcase of $100 bills. Estimate the dollar value in such a suitcase.

Size of $100 note

Let's assume a banknote is about the same thickness as paper; Australian notes are probably a little bit thicker. A 500 page ream of paper is about 5cm tall, so each sheet is about 0.01cm thick.

A note is around 15cm long and about 6cm wide.

So the total volume is about \( 15 \rm{cm} \times 6 \rm{cm} \times 0.01 \rm{cm} \approx 1 \rm{cm}^3\).

Volume of a Suitcase

Suitcases come in a lot of sizes; lets consider a small wheely travel suitcase. Standing up it's around 50cm high, by 30cm wide and 30 cm deep. This gives a total depth of 45L, call it 50L.

A quick search online shows this is in a reasonable range; typically they're in the range of 30L to 110L.

Number of notes in a suitcase.

A litre is \( (10 \rm{cm})^3 = 1000 \rm{cm}^3 \).

So the total value of money in the suitcase would be $100 per note × 1000 notes per L × 50L in the suitcase which is $5 million.

Around $5 million sounds like a reasonable estimate.

Weight of the suitcase

To go a little further how much does the suitcase weigh?

An Australian banknote is probably a little thicker than printer paper, which weighs about 100 grams per square meter. So an Australian banknote weighs around .15 m × .06 m × 100 grams per square meter which is about 1 gram.

So the 50,000 banknotes in $5 million weighs about 50kg. This is a reasonably heavy suitcase of money to wheel around, and bit too heavy to bring on a flight (which typically has limits of 20-30 kg per bag).

Checking the data for Australian Banknotes shows that 1 gram of weight for a note is a reasonable estimate.