By “typical” 401k account I mean the money sitting in the account grows at some constant exponential rate, but we also add the same fixed sum to the account every two weeks. In the beginning it’s going to grow approximately linearly, dominated by the additions, and after many years it’s going to grow approximately exponentially, dominated by interest on the total balance.
I’m looking for an expression, so I can fit models based on real account data. I know one could mimic the behavior numerically, period by period, but I can’t fit models to a process like that, only to expressions.
Perhaps this is embarrassingly easy, but I am just not getting it.
You’re looking for the annuity formula, which I’m not going to try to type out. For your model, you may also want to have two period: an annuity period and a growth period.
Though if your payment isn’t going to be a fixed amount, you’ll probably just need to figure it out on a per-deposit-basis in Excel or something.
Please note that 401k balances do not grow at a constant exponential rate. They are subject to market forces, and could even lose value during a given year.
That depends on how they are invested, obviously. If you’re willing to sacrifice potentially higher investment returns, you can invest your 401k funds in assets delivering a fixed or guaranteed return.
But I think the OP is looking for a term to describe a hypothetical model, in which a particular return on investment is simply assumed.