[pliny]

That's not true, you only get to that figure with 5,000 nominal dollars and 6.2% unadjusted interest

  >>> def comp(s, n, i):
  ...     m = 0
  ...     for x in range(n):
  ...             m *= i
  ...             m += s
  ...     return m
  ...
  >>> comp(5000, 77, 1.062)
  8201943.704759633

So there were some abnormal returns (or inheritance) involved.

[xorfish]

https://dqydj.com/sp-500-return-calculator/

Average dividend reinvested and inflation adjusted return between 1949 and 2016 is 7.5%

  >>> def comp(A, n, i):
  ...     m = 0
  ...     for x in range(n):
  ...         m += i**x
  ...     return A/m
  ... 
  >>> comp(9000000, 67, 1.0725)
  6053.012676780852

Assuming costs of 0.25%, she needs to invest a little over 6000 2016 USD per year to get 9 million USD.

[loeg]

I think your program confirms rather than disputes my comment.

[pliny]

My program adds 5000 nominal dollars to a savings account every 'year' and then applies a 6.2% interest rate once a 'year'.

Where is the '2018 dollars'? The account takes the same nominal deposit at year 0 as at year 76.

Where is the adjustment for inflation in the interest rate? The account adds 6.2% every year regardless of that years inflation.

EDIT: The program obviously cannot account for inflation since it has no notion of inflation. If the secretary were depositing 5000 '2018 dollars' in 1947, then the nominal deposit would have to be something like $500. Inflation is usually positive, so money in the past is worth more.

[ascorbic]

6.2% is the average, inflation-adjusted rate.