The Fed says this is a cube of $1 million. They're off by half a million.

At the Federal Reserve Bank of Chicago’s Money Museum, there’s a big transparent cube on display. It’s filled with tightly packed stacks of $\$1$ bills, claiming to contain $\$1,000,000$.

The plaque proudly declares:

Have you ever wondered what one million dollars looks like? You don’t have to wonder anymore because you can see it right in front of you!

But I don’t trust signs. I trust counting.

I turned to Dot Counter, a rigorously engineered visual quantification instrument designed just for this purpose. I went row by row, stack by stack, and clicked my way to the truth.

And here’s what I found:

Assuming each bundle contains $100$ bills*, that’s

$$102 × 8 × 19 × \$ 100 = \$ 1,550,400$$

*The straps on them are blue which is the standard for a stack of $100$ $\$1$ bills. Unless these are some sort of ultra-rare $\$64.5$ bundles. In which case, I have follow-up questions.

So yeah. They’re off by $50\%$.

That’s $\$550,400$ in extra cash.

Hmm 🤔

Imagine the meeting.

“Hey so… we’re $550,400 over budget on the million-dollar cube project.”

Bad at math?

If you knock $2$ from each dimension, the math actually gets kinda close

$$100 \times 6 \times 17 \times \$ 100 = \$ 1,020,000$$

but that wouldn’t look like a cube.

Inflation?

Maybe the Fed is playing the long game.

At the Fed’s $2\%$ inflation target, this cube will be worth $\$1$ million in today’s dollars in:

$$\log_{1.02}(\frac{1,550,400}{1,000,000})=22 \thinspace\text{years}$$

Can’t wait to come back in 2047 and say: “Nice. Nailed it.”

Technicality?

Sure, it does technically contain $\$1,000,000$.

And also $\$550,400$ of bonus money.

Which is kind of like ordering a burger and getting three.

No one’s complaining. But it’s still weird.

How would you make a million dollar cube?

Turns out U.S. dollars are extremely non-cube-friendly. Each bill is $6.14\thinspace\text{in}$ wide by $2.61\thinspace\text{in}$ tall, a nice and even aspect ratio of:

$$\frac{6.14}{2.61} \approx 2.3524904...$$

Each 100-bill bundle is $0.43\thinspace\text{in}$ inches thick.

Best I could do

• $90$ bundles per stack
• $7 \times 16$ stacks
• $90 \times 7 \times 16 \times \$ 100 = \$ 1,008,000$

Which gives you a lovely almost-cube:

• $42.97\thinspace\text{in}$ $(3.58\thinspace\text{ft})$ wide
• $41.76\thinspace\text{in}$ $(3.48\thinspace\text{ft})$ deep
• $38.70\thinspace\text{in}$ $(3.225\thinspace\text{ft})$ tall

Not perfect. Not terrible.

Unlike, you know… this cube.