The same 4% annual rate can produce different balances depending on when interest becomes part of the principal. That does not make every product labelled “compound” a better choice. First, hold the assumptions constant.
Correction — September 22, 2026: This revision corrects the monthly-compounding figures, the claim that the rule of 72 is always within 1%, and the use of percentage points for a balance comparison. Unsupported product and tax generalizations and the old numerical artwork have been removed. This is a mathematical example, not a product recommendation.
Two rate labels
Before the long-term table, try a smaller question: is 4.10% APY higher than a 4.05% annual interest rate, compounded monthly? Comparing just 4.10 and 4.05 skips the labels. The CFPB’s definitions distinguish APY, which includes compounding, from an interest rate that does not.
These are fictional rate labels, not quotations from banks. Assume the same $10,000 stays deposited for 12 months, both rates remain fixed, all interest stays in the account, and there are no contributions, withdrawals, fees or taxes. Round only the final balances to cents.
A — 4.10% APY: the one-year balance is $10,410.00.
B — 4.05% nominal annual interest, compounded monthly: the APY is approximately 4.12603%, using 100 × [(1 + 0.0405/12)^12 − 1]. The one-year balance is $10,412.60. The APY is rounded for display and entry; these five decimal places reproduce this one-year balance to the cent.
B is ahead by $2.60 before fees and taxes, despite its smaller-looking rate number. That is a small modeled difference, not a recommendation to move money. If B alone charged a hypothetical $3 year-end fee, subtracting it would leave $10,409.60—40 cents below A. Our calculator does not have a fee input; that subtraction is separate arithmetic, not an extra calculator feature.
Check the one-year example
1. Set the scenario. Open the U.S. interest calculator and choose Savings. Set Principal / Lump sum to 10000, Monthly contribution to 0, and Term (months) to 12. Leave After-tax off.
2. Compare the right inputs. Enter 4.10 in APY (%), then 4.12603. Compare the month-12 schedule balances: $10,410.00 and $10,412.60. Entering 4.05 as APY instead gives $10,405.00; that tests a different assumption from B’s nominal-rate label.
3. Check the actual terms. If a real account already gives an APY, do not add monthly compounding again. Confirm its rate duration, balance conditions, fees and access terms before comparing. If the compounding basis is unclear, ask for the account’s disclosed APY rather than guessing it.
Use fictional inputs to try this. The tool puts inputs in its URL; do not enter private financial details. These constant-rate figures do not predict a variable-rate account’s return or decide which account suits you. The older table below answers a different question: what happens when the same nominal 4% uses different compounding frequencies?
Set up a fair comparison
Assume an initial $100,000, a fixed nominal annual rate of 4%, no additional deposits or withdrawals, and no taxes or fees. All compound interest is reinvested. Keeping that rate unchanged for 30 years is a modelling assumption, not a forecast or a promise of purchasing power.
Simple interest is calculated on the original principal. Compound interest also earns interest on accumulated interest; compare the SEC Investor.gov definition.
The balances side by side
| Years | Simple | Annual compounding | Monthly compounding |
|---|---|---|---|
| 1 | $104,000.00 | $104,000.00 | $104,074.15 |
| 5 | $120,000.00 | $121,665.29 | $122,099.66 |
| 10 | $140,000.00 | $148,024.43 | $149,083.27 |
| 30 | $220,000.00 | $324,339.75 | $331,349.80 |
Only final amounts are rounded to cents. At 30 years, monthly compounding exceeds simple interest by $111,349.80. At five years the difference is $2,099.66. Never mix examples with different holding periods when comparing the effect.
Reproduce the calculation
Let P be principal, r the annual rate as a decimal, t years, and n the number of compounding periods per year:
- Simple balance:
P × (1 + r × t) - Compound balance:
P × (1 + r/n)^(n × t) - Annual compounding uses n=1; monthly uses n=12.
The monthly 30-year example is 100000 × (1 + 0.04/12)^360. This is a lump-sum formula, not a formula for regular contributions. With additional deposits, each deposit’s timing matters.
Reproduce the monthly figure in PiPi’s U.S. calculator
The U.S. interest calculator asks for APY, not the nominal 4% interest rate in the table. Under CFPB Regulation DD § 1030.2(c) and (o), APY reflects compounding, whereas the stated interest rate does not. For this monthly-compounding example, the corresponding APY is 100 × [(1 + 0.04/12)^12 − 1] ≈ 4.07415429%.
- Choose Savings, enter $100,000 as Principal, $0 as Monthly contribution, and 360 months as the Term.
- Leave the after-tax option off and type 4.07415429 into the APY (%) field. The modeled final balance is $331,349.80, matching the monthly column to the cent.
- If you enter 4.00 as APY instead, the final balance is $324,339.75. That matches the annual-compounding column at 30 years, not the nominal-4%-with-monthly-compounding column.
The U.S. tool does not directly switch among simple, annual, and monthly compounding. Use the formulas above for all three columns; the APY conversion only lets its savings model reproduce this particular monthly example. These are hypothetical rates, not a bank quote.
The rule of 72 is an estimate
Divide 72 by the annual percentage rate to estimate doubling time. The theoretical annual-compounding value is ln(2) / ln(1+r).
| Annual rate | Rule of 72 | Annual-compounding value |
|---|---|---|
| 2% | 36 years | 35.0028 years |
| 4% | 18 years | 17.6730 years |
| 6% | 12 years | 11.8957 years |
| 8% | 9 years | 9.0065 years |
| 10% | 7.2 years | 7.2725 years |
The relative time error is about 2.85% at 2% and 1.85% at 4%, so “always within 1%” is incorrect. The formula interpolates time; a contract crediting interest only at year-end needs a separate check of the first payment date at which the balance doubles.
An estimated 18 years to double at 4% does not mean quadrupling in 30 years. Two doublings take roughly 36 years. Taxes and compounding frequency are not the explanation for that arithmetic mistake.
Percent is not percentage points
After 30 years, monthly compounding produces about $7,010.05 more than annual compounding. Relative to the annual-compounding balance, this is about 2.16%. It is not “7 percentage points”: percentage points describe subtraction between two percentages, not two account balances.
What the example leaves out
Real comparisons must account for taxes, fees, rate changes, early-withdrawal terms, interest payment dates and whether reinvestment is available. This article does not forecast a fund’s returns or assert which account has the best tax treatment.
Verification scope: the numerical examples were reproduced in automated tests and the APY handoff was checked against the current calculator code. That is not professional financial advice or a completed human fact-check of every claim.