## Sunday, January 26, 2014

### Checking Maynard's arithmetic

In the previous post I quoted Keynes on the growth of capital. He said \$1 grew into \$100,000 in 350 years. (He actually used Pound signs, but I'm lazy.)

He said it was a growth rate of about 3.25 percent.

He also said 250 years, but that was a mistake. After I got confidence that it was 350 years and I understood it right, I looked at the numbers:

I put the value 1 in cell A1.
I put the value 1.0325 in cell B1.
I put the formula =A1*\$B\$1 in cell A2.
I copied cell A2 to the range of cells starting with A3 and ending with A350.

I know, it's only 349 years...

I had to increase the growth rate value in cell B1.

For a growth rate multiplier of 1.0335 I get 98,709.25 in cell A350, just a bit under the 100,000 target value.

For a growth rate multiplier of 1.0336 I get 102,099.29 in cell A350, just a bit over the target value.

I get a growth rate between 3.35% and 3.36%, close enough to the given number 3¼.

I recreated the thing in a Zoho spreadsheet so I could post it here. You can fiddle with it, change any numbers you want. If you mess it up too much, just refresh the page, and Zoho will reload my original sheet for you.

To look at what I'm trying to show you, just tweak the 1.0325 number in the yellow cell, cell B1. Change that number to 1.0335 and you should get 98,709.25 like I got in the OpenOffice sheet. Change it to 1.0336 and you should get 102,099 and change. So you know the growth rate number is somewhere between 1.0335 and 1.0336.

The other yellow cell is for checking what I quoted from the Japanese translation, in a comment on the previous post.

The guy said "250 square of 1.0325" is "about three thousand". I got 2968 and change: about 3000.

Then he increased the start-value from 1.0 to 40 thousand pounds, multiplied his "about 3000" by 40,000, and realized that the answer (120 with six zeroes after it) was nowhere near Keynes's 4 billion number.

Here's the Zoho sheet:

The thing I love most about Zoho is that it includes the formula bar. So you can click on a cell that you want to know about, then look at the formula bar and see the formula in that cell. Usually you can't do that online. Zoho is great!