Simple vs. compound interest
Compare simple and compound interest using clear formulas, the same worked example and a side-by-side table.
The key difference
Simple interest is always calculated on the original principal. Compound interest adds earnings to the balance, so later interest is calculated on both the principal and accumulated interest.
Put another way, simple interest grows linearly; compound interest can accelerate over time. If you want a conceptual introduction first, read what compound interest is.
Simple interest formula
I = P x r x t
ending balance = P + II is interest, P is principal, r is the rate per period as a decimal and t is time. Investing $10,000 at 8% simple annual interest for 10 years gives:
I = 10000 x 0.08 x 10 = 8000
ending balance = 10000 + 8000 = 18000Compound interest formula
FV = P x (1 + r / n) ^ (n x t)n is the number of compounding periods per year. The exponent captures the defining feature of compounding: every period starts from the balance left by the previous one.
For a closer look at each variable, see the compound interest formula.
Comparing the same principal, rate and term
Using $10,000, an annual rate of 8% and a 10-year term:
simple interest: 10000 + (10000 x 0.08 x 10) = 18000
annual compounding: 10000 x (1 + 0.08) ^ 10 = 21589.25
monthly compounding: 10000 x (1 + 0.08 / 12) ^ 120 = 22196.40| Method | Approximate ending balance |
|---|---|
| Simple interest | $18,000.00 |
| Compound interest, annually | $21,589.25 |
| Compound interest, monthly | $22,196.40 |
The starting amount, stated rate and term are identical. Only the treatment of interest changes.
Side-by-side comparison
| Feature | Simple interest | Compound interest |
|---|---|---|
| Calculation base | Original principal | Principal plus accumulated interest |
| Growth pattern | Linear | Accelerates over time |
| Sensitive to reinvestment | No | Yes |
| Effect of time | Adds the same interest each period | Can increase the interest earned each period |
| Typical examples | Classroom estimates, some fixed-interest arrangements | Savings, investments and revolving balances |
Use simple interest when the calculation explicitly keeps the original principal as its base. Use compound interest when earnings are reinvested or unpaid interest becomes part of a balance.
The distinction also applies to borrowing: accumulated interest can work against the borrower. Always check the actual contract because product rules, fees and payment timing may matter more than a textbook label.
Compare scenarios
Use the compound interest calculator to change the rate, term and compounding frequency. For a quick estimate of doubling time, try the Rule of 72.
Frequently asked questions
Which one produces more money?
With the same positive rate, principal and term, compound interest generally produces more because earnings are reinvested. The difference grows with time and more frequent compounding.
Can compound interest apply to debt?
Yes. When unpaid interest is added to the outstanding balance, it may become part of the base for future interest.
What does it mean to capitalize interest?
It means adding interest to the balance. Once capitalized, that amount can affect interest calculations in later periods.