The mechanics
A return can compound when it stays invested.
Compounding describes how a return on an invested balance can itself remain in the balance and be part of later periods’ calculations. It is arithmetic, not a promise that returns will be positive or repeat at a constant rate.
01 / FIELD NOTE
A repeated-period model
If a balance B earns rate r over a period and no money is added or removed, the next balance is B × (1+r). Applying the same rate for n periods gives B × (1+r)^n. A real account does not usually earn the same rate in every period; a flat rate is used here only to make the relationship understandable.
02 / FIELD NOTE
Deposits start earning at different times
Money deposited at a period’s end is exposed to fewer modeled periods than money already in the account. The calculator uses equal deposits at month-end. For comparisons, keep the contribution total and dates explicit; changing the timing changes the result even if the annual dollar total appears similar.
03 / FIELD NOTE
Annual effective return and monthly conversion
The tool treats the annual input as an effective annual rate and converts it to a monthly effective rate using (1+R)^(1/12)−1. This makes twelve identical monthly periods multiply to the stated annual factor. It is different from dividing an annual nominal rate by twelve. The displayed result follows the tool’s stated convention.
04 / FIELD NOTE
Zero, negative, and volatile returns
At zero return, the future value is simply the starting amount plus deposits. A negative constant return can reduce a balance. Neither case captures a market sequence where returns rise and fall, nor does a single average reveal the effect of a loss near a withdrawal date. An investment’s actual value may be lower than the amount invested.
05 / FIELD NOTE
Compounding is only one part of growth
Taxes, fees, the investment mix, inflation, deposit interruptions, and withdrawals affect what remains for future periods. Plan and IRA rules determine what may be contributed and when. The basic formula contains none of those account-specific facts, so it should be read as a mathematical explanation rather than an account projection.