The formula
With a starting balance P, a monthly addition A and a monthly rate r, the balance after n months is:
P × (1 + r)ⁿ + A × ((1 + r)ⁿ − 1) ÷ r
Uphill takes r from the yearly return R as the twelfth root of (1 + R), minus one, so twelve months of growth make exactly R. Each addition goes in at the end of its month.
Why the curve bends upwards
Growth earns growth. In the first years most of the balance is what you added; later, what the money earns each month can overtake what you add. The growth per month card shows the month that happens.
Questions
- What return should I use?
- That is your call, and it is only an assumption. A savings account pays a few percent; a broad stock index has averaged more over long periods, with years far below it. Try a few rates and watch how much the goal dates move.
- Does it account for inflation?
- Turn on today's money and every figure is shown at today's prices, with the inflation rate you choose taken out.
- Monthly or yearly compounding?
- Monthly, with the yearly rate spread so that a full year earns exactly what you set, and your addition going in each month.