Comparing growth...
Enter one principal, rate, and time period to compare both interest methods.
What Is a Simple vs Compound Interest Calculator?
A simple vs compound interest calculator applies both interest methods to one principal, annual rate, and time period. Matching those inputs creates a fair comparison: the only extra setting is how often compound interest is added to the balance. The results show the final balance, interest earned, difference between methods, effective annual rate, formulas, and growth over time.
Simple interest grows by the same monetary amount each year because it always uses the original principal. Compound interest uses a changing base: once interest is credited, later periods can earn interest on that earlier interest. That difference is often small over short periods but can become substantial when a positive rate continues for many years.
Simple Interest Formula and Example
The simple interest balance formula is A = P(1 + rt). In this formula, P is the original principal, r is the annual rate written as a decimal, and t is time in years. Interest alone is I = Prt. Compounding frequency does not appear because the standard simple-interest model never adds earned interest to the principal base.
For $1,000 at 10% for five years, simple interest is $1,000 x 0.10 x 5 = $500. The final balance is $1,500. Each year contributes exactly $100, which creates a straight line when balance is plotted against time.
Compound Interest Formula and Example
The compound interest formula is A = P(1 + r/n)^(nt), where n is the number of compounding periods per year. Annual compounding uses n = 1, quarterly uses 4, monthly uses 12, and daily uses 365. Interest earned is the final balance minus the original principal.
For the same $1,000 at 10% compounded annually for five years, the balance is $1,000 x 1.10^5 = $1,610.51. The first year still earns $100, but the second year earns $110 because the new base is $1,100. Each later interest amount is calculated from a larger balance.
How Simple and Compound Interest Grow Differently
This data chart uses $1,000 at 10% for five years with annual compounding.
| Year | Simple balance | Compound balance | Gap |
|---|---|---|---|
| 0 | $1,000.00 | $1,000.00 | $0.00 |
| 1 | $1,100.00 | $1,100.00 | $0.00 |
| 2 | $1,200.00 | $1,210.00 | $10.00 |
| 3 | $1,300.00 | $1,331.00 | $31.00 |
| 4 | $1,400.00 | $1,464.10 | $64.10 |
| 5 | $1,500.00 | $1,610.51 | $110.51 |
How Compounding Frequency Changes the Result
Compounding frequency determines how many times a year interest is credited. More frequent crediting gives each portion of interest more time to earn additional interest, so a positive nominal rate usually produces a slightly higher effective annual rate. At a 5% nominal rate, monthly compounding has an effective annual rate of about 5.116%, while annual compounding remains exactly 5%.
Frequency is not usually the dominant input. Principal, rate, and time can have much larger effects than changing monthly compounding to daily compounding. Compare products using effective annual rates where available, and also account for fees, restrictions, risk, and changing rates.
When Simple Interest and Compound Interest Are Used
Simple interest is common in classroom finance problems and can describe some short-term lending arrangements. Compound interest is used to model many savings balances, investments, credit products, and debts because credited interest changes the balance used in later periods. A real contract may use daily balances, exact calendar dates, payment schedules, fees, or a day-count convention that this educational model does not include.
This calculator accepts fractional years and applies the closed-form exponent n x t. That is a consistent mathematical convention, but a bank statement may calculate partial periods from exact dates. Investment returns also vary and are not guaranteed merely because a fixed-rate example produces a smooth curve.
Simple vs Compound Interest Comparison Table
| Feature | Simple interest | Compound interest |
|---|---|---|
| Interest base | Original principal | Principal plus accumulated interest |
| Growth pattern | Linear | Exponential at a positive fixed rate |
| Standard formula | A = P(1 + rt) | A = P(1 + r/n)^(nt) |
| Frequency effect | None in the standard formula | Changes the effective annual yield |
| Annual interest amount | Constant | Usually increases as the balance grows |
| Best comparison input | Same principal, rate, and time | Same principal, rate, and time |
Simple and Compound Interest FAQ
What is the difference between simple and compound interest?
Simple interest is calculated only from the original principal, so it adds a constant amount at a fixed rate. Compound interest uses the growing balance, allowing previously credited interest to earn additional interest.
What is the formula for simple interest?
Interest alone is I = Prt, and the final balance is A = P(1 + rt). The annual rate must be converted from a percentage to a decimal before substitution.
What is the formula for compound interest?
The standard periodic formula is A = P(1 + r/n)^(nt). The value n identifies how many compounding periods occur each year.
Is compound interest always better than simple interest?
No. The preferred method depends on whether you are earning or paying interest, and the mathematical values can be equal in several cases. This calculator reports the actual relationship instead of assuming compound interest is always higher.
How often should interest be compounded?
More frequent compounding increases the effective yield at a positive nominal rate, but product fees and terms may matter more. Compare effective annual rates and the complete account conditions.
What does monthly compounding mean?
Monthly compounding divides the nominal annual rate into 12 periodic rates and credits interest 12 times a year. Each credited amount becomes part of the base used in later months.
When do simple and compound interest give the same result?
They are equal when time is zero or the rate is zero. With annual compounding, they are also equal at exactly one year because both methods apply the annual rate once.
How do I compare two interest rates fairly?
Use the same principal, duration, cash flows, and risk assumptions. When compounding frequencies differ, compare effective annual rates rather than nominal rates alone.
Does this calculator include monthly contributions?
No. It deliberately uses one starting principal to isolate the difference between simple and compound growth. Use the Compound Interest Calculator below when you need recurring deposits.
Why might my bank balance differ from this calculation?
Financial institutions may use exact dates, daily balances, fees, changing rates, rounding rules, or specific day-count conventions. This calculator applies standard textbook formulas to the values entered.
Related Calculators
Compound Interest Calculator
Model compound growth with optional monthly contributions.
Percentage Calculator
Solve percentage-of-number and part-to-whole questions.
Percentage Increase / Decrease
Calculate directional changes from an original value.
Percentage Difference Calculator
Compare two values relative to their average.
Rounding Calculator
Round financial results to decimal places or significant figures.
Scientific Notation Converter
Convert very large or small values into scientific notation.