The simple interest formula is I = P × r × t: interest equals the principal multiplied by the annual interest rate (as a decimal) and the time in years. Borrowing or saving $10,000 at 5% for 3 years gives 10,000 × 0.05 × 3 = $1,500 of interest, for a total of $11,500. Simple interest is always calculated on the original amount only.
What do the letters in I = P × r × t mean?
| Symbol | Meaning | How to enter it |
|---|---|---|
| I | Interest, the money earned or owed | Dollars |
| P | Principal, the starting amount | Dollars |
| r | Annual interest rate | Decimal: 5% = 0.05 |
| t | Time | Years: 6 months = 0.5 |
OpenStax defines the same formula for a loan or investment and adds that the total, or future value, is the principal plus the interest: FV = P + I = P + P × r × t. Two details cause most errors. The rate has to be written as a decimal (divide the percentage by 100, see the percentage guide), and the rate is an annual rate, so the time must be measured in years, whatever the actual term.
Worked example: savings and loans
$2,500 lent at 4.5% for 3 years:
- Convert the rate: 4.5% = 0.045.
- Multiply: 2,500 × 0.045 × 3 = $337.50 of interest.
- Add the principal: 2,500 + 337.50 = $2,837.50 in total.
The year-by-year interest is the same each time ($112.50), because the base never changes. That constant amount is what makes the growth a straight line.
How do you solve for principal, rate or time?
Because the formula is a product of three numbers, any one of them can be isolated by dividing the interest by the other two.
| To find | Formula |
|---|---|
| Interest | I = P × r × t |
| Principal | P = I ÷ (r × t) |
| Rate | r = I ÷ (P × t) |
| Time | t = I ÷ (P × r) |
Take a loan that produced $1,350 of interest over a known term at a known rate:
- Time: $9,000 at 3% earned $1,350. t = 1,350 ÷ (9,000 × 0.03) = 1,350 ÷ 270 = 5 years.
- Rate: the same $9,000 over 5 years. r = 1,350 ÷ (9,000 × 5) = 0.03, or 3%.
- Principal: a 3% rate over 5 years. P = 1,350 ÷ (0.03 × 5) = $9,000.
The three answers check each other: plugging any set back into I = P × r × t returns $1,350. A quick way to catch mistakes is to run this reverse check every time.
How do you calculate simple interest for months or days?
The rate is annual, so shorter terms need a fraction of a year.
- Months: divide by 12. Four months is t = 4 ÷ 12, and 18 months is t = 1.5.
- Days: divide by 365 (the "exact" method) or by 360 (the "ordinary" or banker's convention).
OpenStax uses a 365-day year for daily interest and notes that banks have sometimes used and still use 360. The 360-day version produces slightly more interest, because the same annual rate is spread over fewer days:
| $10,000 at 6% for 90 days | Calculation | Interest |
|---|---|---|
| 365-day year | 10,000 × 0.06 × 90 ÷ 365 | $147.95 |
| 360-day year | 10,000 × 0.06 × 90 ÷ 360 | $150.00 |
| Months (3 ÷ 12) | 10,000 × 0.06 × 0.25 | $150.00 |
The difference is $2.05 on this example. It stays small on short terms but grows with the amount and the number of days, so the contract or account agreement is the place to check which day count applies.
How is simple interest different from compound interest?
Under simple interest the base stays at the original principal. Under compound interest, as the CFPB explains, interest is earned on the money saved and on the interest earned along the way. The first year is identical; the gap opens after that. For $10,000 at 5% (compounded annually):
| Years | Simple interest | Compound interest | Difference |
|---|---|---|---|
| 1 | $500.00 | $500.00 | $0.00 |
| 3 | $1,500.00 | $1,576.25 | $76.25 |
| 5 | $2,500.00 | $2,762.82 | $262.82 |
| 10 | $5,000.00 | $6,288.95 | $1,288.95 |
| 20 | $10,000.00 | $16,532.98 | $6,532.98 |
Simple interest adds the same $500 every year, so doubling the money takes 20 years at 5%. Compounding doubles it sooner. The compound interest glossary entry has the compound formula, and the compound interest calculator lets you test other rates and compounding frequencies. Savings accounts and credit cards generally compound; the same rate can therefore cost or earn very different amounts depending on the method, which is why the APY exists as a like-for-like figure for savings.
Where is simple interest used in real life?
Simple interest appears wherever interest is calculated on a balance that does not itself grow with interest.
- Auto loans. The CFPB describes simple interest, based on the outstanding balance of the loan, either daily or monthly, as far more common than precomputed interest. With the daily method, the lender applies a periodic rate to the outstanding balance each day, as the Federal Reserve's vehicle guide describes. A loan of $18,000 at 7% accrues about 18,000 × 0.07 ÷ 365 = $3.45 of interest per day at the start; over a 30-day stretch that is about $103.56.
- Short-term notes and some personal loans. One flat rate on the principal for a stated period.
Why does the payment date matter on a daily simple interest loan?
Interest accrues on whatever is still owed each day. The Federal Reserve notes that paying before the due date means paying less interest in total, while paying after it, even inside a grace period, means paying more. Extra principal payments reduce the balance on which later interest accrues. With precomputed interest, the CFPB points out, the total interest is calculated up front and extra payments do not reduce it, so it is worth checking the loan type before paying a loan off early.
Common mistakes with the simple interest formula
- Using the percentage instead of the decimal. Entering 5 instead of 0.05 makes the interest 100 times too large.
- Using months as years. 18 months is 1.5 years, not 18.
- Applying simple interest to a compounding account. A credit card or savings account balance with monthly compounding will not match I = P × r × t.
- Forgetting the day-count convention. A 360-day lender and a 365-day lender produce slightly different daily interest on the same rate.
- Confusing interest with the total. I is only the interest; the amount owed or earned is P + I.
This guide is educational and not financial advice; a loan or account agreement controls how interest is actually calculated.