Let earlier interest join the balance
Compound interest means that accumulated interest also earns interest. To see the mechanism, use a fixed hypothetical rate and add each year's interest to the balance before calculating the next year. This isolates compounding from the separate effect of making new contributions.
The rate in an illustration is an assumption, not a forecast or promise. Real accounts and investments can have variable rates, fees, taxes and different risks. A smooth table describes its inputs faithfully; it does not establish that the real world will follow them.
Build three rows by hand
Start with $1,000 and assume exactly 5% interest credited annually, with nothing added or withdrawn. Year one earns $50 and ends at $1,050. Year two earns $52.50 and ends at $1,102.50. Year three earns $55.125 before rounding, giving approximately $1,157.63 at the end.
The first year's $50 helps generate $2.50 of the second year's interest. By comparison, simple interest on the original $1,000 at 5% for three years would add $150, ending at $1,150. The approximately $7.63 difference comes from earning interest on prior interest under these assumptions.
Separate growth from contributions
If you also deposit $100 at the end of each year, those deposits change the outcome and their timing matters. A deposit made on the final day cannot earn the same full-year interest as money present at the beginning. Label contributions and interest as separate columns rather than calling every increase a return.
Use the model for questions
Try changing one input at a time: the starting amount, contribution or time period. Keep rounding to the final display where possible, unless you are reproducing an account's stated rounding method. Use the resulting figures to understand sensitivity and plan contributions, while checking the actual product terms before relying on any projected balance for a spending commitment. Avoid adding projected interest to a spending plan as though it has already been credited and become available.
