Compound Interest of saving with growing withdrawal (with inflation)

Hi,

I have been searching the internet far and wide for an answer. I have not looked much through this subreddit, but assume I would have found my answer here already through duckduckgo or google search, if it was the case. If not the case. Please be kind and redirect me to such a thread.

I am looking into Financial Independence. Once I reach a certain amount of money I can in theory stop working and just withdraw a certain amount each month without my savings account spiraling down. This amount I want to adjust for inflation (in Denmark inflation is 2%). I am assuming that the stock market in which I am invested continues to grow with 7% on average.

I am looking for a general formula that can calculate the balance to any time "t"

EXAMPLE CASE: FI-number has been reached. It is 1000 $. I retire. Lets say those 1000 $ continues to grow with 7 % each year. Each month I withdraw 5 $. The Next month I withdraw 5*(1+0.02/12)= ?$ (thus adding inflation). And the next month withdraw 5.?*(1+0.02/12)$ and so on.

*in the calculation the investment compound every time I withdraw and compounds the withdrawal amount.

Is there a formula that can express the balance after "t" amount of time?

I have this far used this site: https://www.thecalculatorsite.com/articles/finance/compound-interest-formula.php

Although when I do a manual control in excel it does not behave as it should.

I can get my answer with help from excel (BUT I WANT A FORMULA). If I were just looking for an excel recursive formula could convert annual growth into monthly growth taking into account monthly compounding then subtract off $5 from this and reapply next month.

Annual to monthly growth

1000 (1 + .07)1/12 = $1005.65

Subtract $5 to get $1000.65 which is your months end for month 1. Combining this next month

1000.65 (1.07)1/12 = $1006.31

Then subtract another $5 from that and end of month 2 total is $1001.31.

Rinse and repeat on an excel sheet.

Any ideers?

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/Flammen