Hypothetical worked example and primary educational references; not observed market data.
Follow the base rather than the label
The defining difference between simple and compound interest is the amount used to calculate the next period's interest. Under simple interest, the original principal remains the base. Under compound interest, retained earnings expand it. CFPB's explanation establishes the interest-on-interest mechanism; this article compares it with an intentionally fixed base. A product name alone is insufficient to identify the cash-flow pattern. Interest might accrue on one schedule, be credited on another, and be distributed to a different account. Drawing the path of earnings clarifies what actually compounds. The relevant question is where each interest payment goes and whether that location participates in the next period's calculation.
Supporting references: 1. CFPB: How compound interest works
Simple growth is linear in time
For principal P, annual simple rate r, and t years, accumulated interest is P multiplied by r multiplied by t. Add that interest to principal to obtain the combined principal-plus-distribution total, assuming every distribution is retained without further earnings. Each additional year adds the same amount. In the hypothetical example, an USD 8,000 principal at three percent generates the same annual interest base over six years. This is a mathematical arrangement, not a description of a particular account. The simple total includes the accumulated interest even though it does not earn more interest. Otherwise a comparison against a compounded balance would omit cash received and unfairly favor one accounting presentation.
Hypothetical worked example
An untouched deposit under two growth rules
Model setup
Read these assumptions before comparing the scenarios.
- All monetary amounts in this example are hypothetical U.S. dollars (USD), not current prices, quoted account terms or observed market data. Percentages, counts, time periods and index levels retain their stated units.
- Initial principal is a hypothetical USD 8,000.
- Annual rate is 3% for six years.
- Simple interest stays outside the interest-bearing base; compound interest stays inside.
Year-end value (USD), USD 8,000 start, 3% annual rate
- Simple interest total
- Compound interest total
Period-by-period model values (USD)
| Year | Simple interest total | Compound interest total |
|---|---|---|
| 0 | 8,000.00 | 8,000.00 |
| 1 | 8,240.00 | 8,240.00 |
| 2 | 8,480.00 | 8,487.20 |
| 3 | 8,720.00 | 8,741.82 |
| 4 | 8,960.00 | 9,004.07 |
| 5 | 9,200.00 | 9,274.19 |
| 6 | 9,440.00 | 9,552.42 |
Intermediate points are independently calculated from the same fixed example assumptions; zero-based vertical scale. No changing rates, fees or taxes.
Hypothetical model, not observed market data or a forecast. Assumptions above; original values and calculations below.
| Hypothetical scenario | Calculated result (USD) |
|---|---|
| Simple interest total | 9,440.00 |
| Annual compound total | 9,552.42 |
Calculation details
- Simple interest total
- 9,440.00 USD
(8000 * (1 + (0.029999999999999999 * 6))) - Annual compound total
- 9,552.42 USD
(8000 * (1.03 ^ 6))
Compound growth uses successive factors
With annual compounding, multiply principal by one plus the annual rate raised to the number of years. The second year's interest is calculated on the original deposit plus the first year's interest. Later periods repeat that update. The rate can remain unchanged while the money added each year increases because the base is growing. This is why the phrase a constant return can be ambiguous: a constant percentage does not imply a constant cash addition. The two example rows maintain the same invented rate and duration. Their difference comes solely from the treatment of earned interest, making it possible to explain the mechanism without attributing anything to changing market conditions.
A distribution can compound somewhere else
Suppose interest leaves the original account but is placed into a second interest-bearing account. The first balance may follow a simple-interest pattern while the combined household savings compound through the second balance. Conversely, an account can compound internally while repeated withdrawals prevent the household from accumulating much wealth. Account-level arithmetic and household-level arithmetic therefore need different boundaries. Specify which balances are included and whether distributions are saved or spent. For comparing total resources, include every cash flow exactly once. For reconstructing an account statement, include only the cash flows entering or leaving that account. Confusing these boundaries can make a legitimate distribution look like missing interest or make spending look like poor account performance.
Inspect the contract and test a limiting case
US account-disclosure rules address the frequency of compounding and crediting and the methods used to determine interest-bearing balances. Those details matter more than a generic label. A quick model check is to use a one-year horizon with annual compounding: simple and compound totals should match when the rate and base match. At zero interest they should also match for every horizon. Differences emerge only when earnings have time to earn further interest. These checks catch formula mistakes without requiring a product recommendation. The six-year illustration assumes unchanged rates and no charges, so its neat result teaches an accounting distinction rather than promising that any real savings balance will follow that exact path.
Supporting references: 2. CFPB: Regulation DD account disclosures
Test another situationFollow distributed interest into the second account
A separate hypothetical case. Its inputs differ from the main worked example above.
Follow distributed interest into the second account
In an independent hypothetical scenario, USD 3,000 earns simple annual interest of 10% for two years. The first USD 300 distribution arrives at the end of year one and goes into a separate account earning an invented 5% over year two. The second USD 300 arrives at the final valuation date. Combined resources are exactly USD 3,615: original principal, the first distribution grown to USD 315, and the final distribution. Retaining earnings at the original 10% would instead produce USD 3,630. Keeping income outside the original base therefore sacrifices USD 15 of growth under these assumptions, in exchange for the separate account's stipulated use and earning schedule.
Use an account inventory to detect missing or repeated payments
Investor.gov's growth calculator separates initial money and contributions. Extend that distinction across accounts by marking each interest distribution as retained, transferred, or spent. A transfer reduces one account and increases another; it cannot create another household receipt. Adding both cumulative distributions and the receiving account's full balance would count the original first distribution again. Inspect combined balances at the same date and trace each payment exactly once. A simple-interest account can coexist with household compounding elsewhere, but the household result depends on what the receiving account actually earns and when each distribution arrives, rather than on the original account's label alone.
Supporting references: 3. SEC Investor.gov: Compound Interest Calculator
Check this case’s calculations
- Correct combined resources
- 3,615.00 USD
((3000 + (300 * 1.05)) + 300) - Retained-interest alternative
- 3,630.00 USD
(3000 * (1.1000000000000001 ^ 2)) - Growth sacrificed
- 15.00 USD
((3000 * (1.1000000000000001 ^ 2)) - 3615) - First distribution after receiving-account growth
- 315.00 USD
(300 * 1.05)
Limits of this additional case
- Receiving-account growth is assumed constant; taxes and distribution delays are excluded.
Limits of this analysis
- Actual deposit interest methods require the agreement.
- Distributed interest may earn a separate return not modeled here.
- Taxes and fees could alter both paths.
Sources and scope
- CFPB: How compound interest works
Interest can earn additional interest when retained.
Scope: US consumer education; numerical extensions here are independently constructed.. Reference accessed 2026-10-06.
- CFPB: Regulation DD account disclosures
Covered account disclosures address rates, balance methods, fees, and time-account conditions.
Scope: US Regulation DD; educational discussion does not establish individual legal rights.. Reference accessed 2026-10-06.
- SEC Investor.gov: Compound Interest Calculator
Growth inputs distinguish initial money, contributions, time, and estimated interest.
Scope: Educational input framework only; the scenario is independent, not a return forecast.. Reference accessed 2026-10-26.
Illustrative calculations are not forecasts or personal recommendations. Editorial standards
