Compound Interest With Monthly Contributions: Why Simulation Beats the Formula

The textbook formula for compound growth assumes one deposit and silence. Real plans look different: an initial amount, a contribution every month, and the question everyone actually asks — how much of the final number is mine versus interest? The Compound Interest Calculator answers that by simulating every period instead of collapsing the math into one formula.

What the simulation actually does

Each compounding period applies two operations in order:

• End-of-period timing: balance grows first, your contribution lands after.
• Beginning-of-period timing: the contribution lands first, then the whole balance grows.

That ordering sounds like a technicality. Over 20 years it typically adds a low single-digit percentage to the final balance — one extra growth period applied to every contribution you ever made.

Compounding frequency changes the answer

A 12% nominal rate produces different effective annual rates (EAR) depending on how often interest compounds: annually ≈ 12.00%, quarterly ≈ 12.55%, monthly ≈ 12.68%. Monthly compounding applies interest-on-interest sooner, and the tool shows the EAR next to the nominal rate so the difference is visible rather than buried.

Reading the gap

The chart overlays cumulative contributions against the growing balance. The widening gap between the two lines is compounding at work: with 10,000 initial + 200/month at 7% for 20 years, roughly half the final balance is interest. The interest-share bar makes the proportion explicit, and the yearly schedule exports as CSV for spreadsheets or advisor meetings.

Where the honest limits are

• Projections assume a constant rate; real returns vary year to year and sequence risk matters for withdrawals.
• The calculator does not model taxes, fees or inflation — treat the output as pre-cost nominal growth.
• Contribution amounts are nominal; entering today's euros means 20-years-later euros.

For the borrowing side of the same coin, the Loan & Mortgage Calculator simulates amortization the same period-by-period way — and its extra-payment analysis is the mirror image of contribution timing here.