How this number is made
This compounds the balance monthly and adds the contribution until the target is hit, or until 80 years pass. The rate is an assumption. A bad sequence of returns can take longer than a smooth rate.
- The target should be in the same dollars as the rate. A nominal rate needs a target that includes inflation.
- The contribution is what you add, not your whole paycheck.
Formula
Each month the balance grows by the monthly rate and then the contribution is added. The result is the first month the balance reaches the target.
Worked example
With the figures already in the form, years to the target is 20.6.
Questions
Why not a formula?
There is a closed form. The loop is the same math and it stops cleanly when the payment cannot catch a target that the growth already passed, or when it never will.
What if I am already there?
The result is zero years.