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Trouble calculating APY

In the attached spreadsheet, I am trying to verify the calculations for APY. The terms are on row 1. The cell in orange has the correct answer.

In the cells below, I am trying to work out the detail and get the detail to reconcile with the orange cell. So first I am just determining interest in column C. Cell F9 has the original amount ($1 in this case) plus interest.

Then in cell F10 I am calculating my yield based on the original amount (C7).

I am close but I am off. What am I missing?

File attached.
 

Attachments

I think your logic is wrong in your table as you are only calculating the Balanmce of the interest on the interest and not including the principal

See attached

Now both systems match
 

Attachments

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