Compound interest, explained with numbers you can check yourself
Why time matters more than rate, what compounding frequency really changes, and the Rule of 72 — with worked figures you can verify.
Compound interest gets described as magic often enough that the actual mechanism gets lost. There is no magic. Each period you earn interest on your balance, that interest joins the balance, and next period you earn interest on the larger number. Everything surprising about it comes from repeating that loop many times.
The loop, one year at a time
Put $10,000 in at 8% a year, compounded annually. Year one earns $800, leaving $10,800. Year two earns 8% of $10,800 — that is $864, not $800. Year three earns $933. The interest itself grows, because the thing generating it grows.
| Year | Starting balance | Interest earned | Ending balance |
|---|---|---|---|
| 1 | $10,000 | $800 | $10,800 |
| 2 | $10,800 | $864 | $11,664 |
| 3 | $11,664 | $933 | $12,597 |
| 10 | $19,990 | $1,599 | $21,589 |
| 20 | $43,157 | $3,453 | $46,610 |
Notice the last row. In year 20 the balance grows by $3,453 — more than a third of the original deposit, in a single year, from money you stopped thinking about two decades ago.
Time beats rate, and it is not close
This is the part worth internalising. Compare two savers, both investing $10,000 at 8%:
- Ada invests at 25 and stops at 35 — ten years of contributions, then nothing.
- Ben starts at 35 and invests every year until 65 — thirty years of contributions.
Ben puts in three times as much money. At 65, Ada is typically still ahead. Her early deposits had forty years to compound; his had a decade or two. The exponent in the formula is time, and no realistic difference in rate compensates for starting late.
What compounding frequency actually changes
Monthly compounding beats annual — but by far less than most people expect. $10,000 at 8% for 10 years gives $21,589 compounded annually and $22,196 compounded monthly. That is a difference of about $600, roughly 3%. Worth having, not worth agonising over. Frequency is a rounding detail; time and rate are the levers.
It runs in reverse too
The same formula describes inflation eating your purchasing power, and credit card interest compounding against you. A card at 22% APR compounds monthly on any balance you carry — which is exactly why minimum payments stretch a modest balance across years. Compounding is indifferent to which direction it works in.
Compound Interest Model your own balance, with a growth chart SIP Calculator See what a monthly investment grows into Inflation Calculator Check what inflation does to the same money