How this number is made
Compound interest is interest credited on earlier interest. A monthly contribution matters because each deposit starts its own compounding clock. The chart is the balance, not a promise that a portfolio will earn the rate you typed.
- Separate money you already have from money you will add.
- Pick a rate you can defend. Cash is not a stock return. A stock assumption is not a savings-account yield.
- Keep the years inside a horizon you will actually leave the money alone.
Formula
With monthly rate r and n months: balance = principal × (1+r)^n + contribution × ((1+r)^n − 1) ÷ r. If the rate is zero, balance = principal + contribution × n.
Worked example
Five thousand dollars plus $300 a month for 20 years at 7% is on the order of $170,000. The cash you deposited is $77,000. The gap is compounding, and it shrinks quickly if the return is 3% instead of 7%. Change the rate and look again.
Questions
Does this include taxes and fees?
No. A taxable account owes tax on interest, dividends, or gains. A fund expense ratio comes out of the return. Use a lower rate if you want a rough after-fee number.
Why monthly compounding?
Contributions are monthly, so the model compounds monthly too. Daily versus monthly changes the result only slightly next to the rate you assume.