Understanding your simple interest results
The following comparison illustrates how simple interest and compound interest diverge over time for the same principal and rate.
| Years | Simple interest (5% p.a.) | Compound interest (5% p.a., annual) |
|---|---|---|
| 1 | 5.00% | 5.00% |
| 5 | 25.00% | 27.63% |
| 10 | 50.00% | 62.89% |
| 20 | 100.00% | 165.33% |
| 30 | 150.00% | 332.19% |
- Simple interest is linear with time; compound interest is exponential. Over short periods the difference is small; over decades it becomes very large.
- For fractional-year periods, this calculator treats time as a continuous decimal. Some loan instruments use day-count conventions (such as actual/360 or actual/365) that can produce slightly different results.
- The simple interest formula does not account for fees, origination charges, or other costs of borrowing, which are incorporated in the APR for consumer loans.
What is simple interest?
Simple interest is the most straightforward method of calculating the cost of borrowing or the return on lending. Interest accrues only on the original principal for the duration of the loan or investment, and is not added to the principal to generate further interest. This makes simple interest calculations linear: doubling the time doubles the interest, and doubling the rate doubles the interest.
Simple interest is used in a variety of financial instruments. US Treasury bills (T-bills), which are short-term government securities with maturities of up to one year, are priced on a simple-interest (discount) basis. Many consumer auto loans and short-term personal loans also use simple interest, where each payment is applied first to the accrued interest for the period and the remainder to the principal.
For time periods longer than one year, or when interest is reinvested, compound interest accumulates more value than simple interest at the same nominal rate. For very short periods (days to weeks), the difference between simple and compound interest is minimal.
How to use this simple interest calculator
- Enter the principal — the initial amount lent, borrowed, or invested.
- Enter the annual interest rate as a percentage.
- Enter the time period in years. Fractional years are accepted (e.g., 0.5 for six months, 1.5 for eighteen months).
- Read the total interest and the final amount (principal plus interest).
The simple interest formula
The simple interest formula multiplies the principal by the annual rate (expressed as a decimal) and by the time in years. The total amount at the end of the period is the sum of the principal and the interest.
자주 묻는 질문
What is simple interest?
Simple interest is interest calculated only on the original principal, using the formula I = P·r·t, where P is the principal, r is the annual interest rate expressed as a decimal, and t is the time in years. Unlike compound interest, simple interest does not accrue on previously earned interest, so the growth is linear rather than exponential.
What is the difference between simple and compound interest?
With simple interest, interest is calculated only on the original principal each period. With compound interest, interest is calculated on the principal plus any previously accumulated interest — so interest earns interest. Over short periods the difference is small; over many years or decades, compound interest grows substantially faster than simple interest at the same nominal rate.
Where is simple interest used in practice?
Simple interest is used in US Treasury bills (T-bills), many short-term consumer and auto loans, some personal lines of credit, and simple savings certificates. It is also used as an approximation for compound interest over very short periods, where the two methods produce nearly identical results.
How do I calculate simple interest for less than one year?
For periods shorter than one year, express the time as a decimal fraction of a year. Six months is 0.5 years, three months is 0.25 years, and so on. For example, $5,000 at 6% for 6 months: I = 5,000 × 0.06 × 0.5 = $150.
참고 자료
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance (13th ed.). McGraw-Hill, 2020. Chapter 2: How to Calculate Present Values.
- US Department of the Treasury. Treasury bills: how T-bills are priced and issued. treasurydirect.gov.
- Consumer Financial Protection Bureau (CFPB). Understanding loan interest. consumerfinance.gov.
- Ross SA, Westerfield R, Jordan BD. Fundamentals of Corporate Finance (12th ed.). McGraw-Hill, 2019. Chapter 5: Introduction to Valuation.