Simple interest calculates interest from the original principal under the stated simple-interest model. Compound interest adds earned interest to the balance, allowing later interest to be calculated on the original principal plus earlier interest.
That “interest on interest” effect is the key difference.
Simple vs. compound at a glance
| Feature | Simple interest | Compound interest |
|---|---|---|
| Interest base | Original principal in the basic model | Principal plus accumulated interest |
| Growth shape with fixed positive rate | Linear | Curved upward over time |
| Basic formula | A = P(1 + rt) | A = P(1 + r/n)^(nt) |
| Compounding frequency matters? | No in basic simple-interest formula | Yes |
| Does this describe every real product? | No | No |
Simple-interest formula
A common simple-interest formula is:
A = P(1 + rt)
Where:
- A = final amount;
- P = original principal;
- r = annual rate as a decimal;
- t = time in years.
The interest amount alone is:
I = Prt
Compound-interest formula
A common compound-interest formula is:
A = P(1 + r/n)^(nt)
Where:
- A = final amount;
- P = original principal;
- r = annual rate as a decimal;
- n = number of compounding periods per year;
- t = time in years.
The SEC’s investor education materials describe compound interest as earning interest on accumulated interest.
Five-year fictional example
Use the same assumptions on both sides:
- principal: $1,000
- annual rate: 5%
- time: 5 years
- compound side: annual compounding
- no deposits or withdrawals
Simple interest
A = 1,000(1 + 0.05 × 5)
A = $1,250.00
Interest earned = $250.00
Compound interest
A = 1,000(1 + 0.05)^5
A ≈ $1,276.28
Interest earned ≈ $276.28
Difference after five years
$1,276.28 − $1,250.00 = $26.28
The difference grows because the compound side begins earning interest on earlier interest.
Year-by-year comparison
| End of year | Simple | Compound annually |
|---|---|---|
| 0 | $1,000.00 | $1,000.00 |
| 1 | $1,050.00 | $1,050.00 |
| 2 | $1,100.00 | $1,102.50 |
| 3 | $1,150.00 | $1,157.63 |
| 4 | $1,200.00 | $1,215.51 |
| 5 | $1,250.00 | $1,276.28 |
The first year matches because no previous interest exists yet to compound.
Why compounding frequency matters
On the compound side, n controls how often interest is added under the model.
At the same nominal annual rate, more frequent compounding can produce a different final amount because interest is added to the balance more often.
The companion tool lets learners compare:
- annual;
- semiannual;
- quarterly;
- monthly;
- daily.
The comparison does not label one compounding frequency as an investment recommendation.
Real products can use different rules
Classroom formulas are useful models, but real financial products can use contract-specific interest methods.
For example, some student-loan servicer materials describe simple daily interest, while capitalization can add unpaid interest to principal under specified circumstances. That is different from assuming an account compounds automatically every month.
Credit cards can also use daily periodic-rate methods.
The math can be taught without claiming that every savings account, loan, or credit card follows one formula.
What changes the result?
For simple interest:
- principal;
- rate;
- time.
For compound interest:
- principal;
- rate;
- time;
- compounding frequency.
The Simple vs. Compound Interest Explorer holds the assumptions side-by-side so a learner can change one input and see the effect.
Common misunderstandings
“Compound interest always means investing.”
No. Compounding is a mathematical process that can appear in different financial contexts.
“Simple interest never changes principal in a real loan.”
Real product rules can include payments, capitalization, fees, and other events.
“5% for five years guarantees this result in an investment.”
No. The example assumes a fixed interest rate purely for math education.
“More frequent compounding is always better for me.”
The direction of benefit depends on whether a person is earning or paying interest and on the actual product terms. FIL does not make the decision.
Try the model
Use the Simple vs. Compound Interest Explorer to enter a fictional principal, rate, time, and compounding frequency. It shows both formulas and a year-by-year table.
Educational boundary
This lesson explains interest math. It does not forecast investment returns, recommend a loan or account, or calculate a specific product’s legally disclosed APR or APY.
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Official sources
These primary sources support the key factual claims on this page. Current rules and program details should always be verified with the issuing agency.