Alternate FIRE Formulas: Compound Interest Solved for Time

I wanted to know when I would have enough money to retire.  I picked a total savings number.  I know how much money I have.  I know what  I choose to “guestimate” my annual average interest rate is; 7%.  So I found the standard compound interest formula here.

Compound Interest formula

Where:
V = future value
P = principle
r = interest rate
n = number of times interest is compounded each year
t = number of years

I then solved it for time.

solve for t

I have not found that anywhere, so if you were curious like me, here it is.

So now you can find out how long it will take you to retire if you don’t add any money each year.  For me, the number was 13 years, assuming a 7% average yield each year. We are due for another recession, but that number should be pretty close.  Still, this does give me a good idea. Modify the formula to account for each additional annual contribution.

But that formula becomes more complicated:

(Compound Interest Formula) × {[(1 + r/n)(nt) – 1] / (r/n)}

At this point, it’s just easier to write a program.  The program would do this each year, and add the principle each year.  I don’t have time to write it today, but consider that forthcoming.

 

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