This worksheet compares one unchanged deposit under two mathematical rules. It adds a year-by-year check to the introductory simple-versus-compound guide. The rate is hypothetical and constant; it is not an investment return forecast.
Fix the assumptions first
- Starting principal: 10,000 currency units.
- Annual rate: 6%, written as 0.06.
- No contributions, withdrawals, fees or tax.
- Compound case: interest credited and retained once a year.
Compare balances, not interest with principal
| Years | Simple balance | Compound balance | Difference |
|---|---|---|---|
| 1 | 10,600.00 | 10,600.00 | 0.00 |
| 5 | 13,000.00 | 13,382.26 | 382.26 |
| 10 | 16,000.00 | 17,908.48 | 1,908.48 |
| 20 | 22,000.00 | 32,071.35 | 10,071.35 |
The simple balance is 10,000 × (1 + 0.06 × years). The compound balance is 10,000 × 1.06years. At 20 years the balances are 22,000 and 32,071.35. Subtract the original 10,000 to compare interest earned: 12,000 versus 22,071.35. The compound balance is not double the simple balance.
Why year one is equal
Both cases start with the same 10,000 and add 600 in the first year. In the second compound year, 6% acts on 10,600, producing 636. The simple case still adds 600. Each later difference follows from the balance on which interest is calculated.
Reproduce this in a spreadsheet
Put the year in A2. Use =10000*(1+0.06*A2) for the simple balance and =10000*(1.06^A2) for annual compounding. Subtract the first result from the second for the gap. Keep full precision in the formulas and round only the displayed amounts.
Change one assumption at a time
Monthly compounding requires a monthly rate and 12 periods per year. Deposits require a separate contribution calculation and a decision about whether each deposit is made at the start or end of a period. Fees, taxes and withdrawals also change the path. Do not compare two calculators until those settings agree.
Use the compound interest calculator with contribution set to zero and annual compounding to reproduce this example. For borrowing with scheduled repayments, see flat versus reducing-balance interest; a shrinking loan balance is a different setup.
What the worksheet cannot show
A fixed-rate curve is arithmetic, not evidence that an investment will earn that rate. Market losses, variable rates and charges are absent. Credit-card and loan interest must be checked against the actual contract; daily accrual should not automatically be described as daily compounding.