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Interest Calculator: Simple and Compound
Enter a principal, a yearly rate and a period of time. Choose simple interest, which grows in a straight line, or compound interest, which earns interest on earlier interest, and see the total.
The two formulas
Simple interest is calculated on the original principal only: I = P × r × t, where P is the principal, r the yearly rate as a decimal and t the time in years. The balance rises by the same amount every year.
Compound interest adds the interest to the balance at each compounding date, so the next period earns interest on a larger amount: A = P × (1 + r ÷ n)n × t, where n is the number of compounding periods per year. The interest earned is A − P.
Both formulas assume the rate and the principal do not change and that no money is added or withdrawn during the period.
Why the two diverge over time
Over one year at the same rate, simple and yearly-compounded interest are identical. The gap appears from year two, when compound interest starts earning on the first year's interest. The gap widens faster the longer the money stays invested and the higher the rate is.
| 1,000 at 5% a year | Simple | Compounded yearly |
|---|---|---|
| After 1 year | 1,050.00 | 1,050.00 |
| After 10 years | 1,500.00 | 1,628.89 |
| After 30 years | 2,500.00 | 4,321.94 |
More frequent compounding helps only a little. Monthly rather than yearly compounding at 5% lifts the effective annual rate from 5.00% to about 5.12%.
Where each type is used
- Simple interest: some short-term loans, certain bonds that pay a fixed coupon, and classroom exercises.
- Compound interest: savings accounts, deposits, most investment growth, credit cards and mortgages.
The same arithmetic works against you when you borrow. A balance that compounds at a high rate can double in a surprisingly short time, so check how a lender or card issuer applies interest before assuming it is simple.
Limits of this calculator
It treats the rate as fixed and ignores fees, taxes and inflation. Real accounts often pay a variable rate, credit interest on a daily balance or round to the nearest cent at each step, which can shift the result slightly. For regular deposits use the compound interest calculator. Results are estimates for learning and planning, not a promise of what an account will pay.
A quick check on your answer
Reverse-check the simple-interest case by hand: principal × rate × time. For terms longer than one year, a compound result should always exceed simple interest at the same rate, because compounding adds interest on interest. Also confirm the time unit: a rate quoted per year must be divided by twelve if you apply it to months.
Worked example
A deposit of 10,000 earns 8% a year, compounded quarterly, and is left untouched for three years.
Inputs
| Principal amount | 10000 |
|---|---|
| Annual interest rate | 8 % |
| Time period | 3 |
| Time is in | Years |
| Type of interest | Compound interest |
| Compounded | Quarterly |
Result
Compound interest, 4 time(s) per year over 3.00 years.
| Principal | 10,000.00 |
|---|---|
| Interest earned | 2,682.42 |
| Interest as a share of principal | 26.82% |
| Interest if it were simple | 2,400.00 |
| Effective annual rate | 8.2432% |
- Compound formula: A = P × (1 + r ÷ n)^(n × t).
Financial disclaimer: Results are estimates for planning and education. They are not financial, tax or legal advice. Fees, taxes, rates and rules vary by lender, product and country, so confirm figures with your provider or a qualified adviser before making decisions.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is paid only on the original principal. Compound interest is paid on the principal plus any interest already added, so the balance grows faster over time.
How do I calculate simple interest by hand?
Multiply the principal by the yearly rate as a decimal and by the number of years. For 5,000 at 6% for 5 years that is 5,000 × 0.06 × 5 = 1,500.
Does compounding more often make a big difference?
Not usually. Moving from yearly to monthly compounding adds a small amount, while the rate and the length of time matter far more.
How do I enter a period shorter than a year?
Choose months as the unit. Six months is treated as half a year in both formulas.
Is the interest I earn the same as my profit after tax?
No. This calculator shows interest before any tax, fees or inflation. Those can reduce what you actually keep.
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References and sources
- Investor.gov (U.S. SEC): educational material on compound interest and saving. Link