How to use this simple interest calculator
- Choose what to solve for: interest, principal, rate or time.
- Enter the other three values. The rate is the annual rate in percent; the principal is the amount borrowed or invested.
- Pick the time unit. For days, choose a 365-day or 360-day year to match your contract.
- Read the answer and the total amount. The table below the result shows how much more the same money would earn with compound interest.
Simple interest formula
I = P × r × t; A = P + I = P × (1 + r × t)
- I
- interest
- P
- principal (the original amount)
- r
- annual interest rate as a decimal (5% = 0.05)
- t
- time in years (months ÷ 12, or days ÷ 365 or 360)
- A
- total amount: principal plus interest
Rearranging the same formula gives each of the other values:
P = I ÷ (r × t); r = I ÷ (P × t); t = I ÷ (P × r)
Worked examples
Find the interest
$10,000 at 5% for 3 years: I = $10,000 × 0.05 × 3 = $1,500.00, and A = $10,000 + $1,500 = $11,500.00.
Find the principal
How much must you invest at 4% to earn $600 in 18 months? Time is 18 ÷ 12 = 1.5 years, so P = 600 ÷ (0.04 × 1.5) = $10,000.00.
Find the rate
A $8,000 loan costs $1,200 in interest over 30 months (2.5 years). The rate is r = 1,200 ÷ (8,000 × 2.5) = 0.06, or 6% a year.
Find the time
How long does $5,000 at 6% take to earn $450? t = 450 ÷ (5,000 × 0.06) = 1.5 years, which is 18 months.
365 vs. 360 days: which day count to use
When time is measured in days, you need the number of days in a year. An actual/365 count divides by 365. A 360-day year (the “banker’s year”) divides by 360, so each day carries 1/360 of the annual rate and the interest comes out about 1.4% higher. For $10,000 at 6% for 90 days:
- 365-day year: $10,000 × 0.06 × 90/365 = $147.95
- 360-day year: $10,000 × 0.06 × 90/360 = $150.00
Deposit accounts are different: Regulation DD requires banks to calculate interest with a daily rate of at least 1/365 of the interest rate (§ 1030.7). For a loan, check the promissory note or disclosures for the day-count method.
Simple vs. compound interest over time
Simple interest adds the same $500 every year on $10,000 at 5%. Compound interest adds interest on interest, so the gap widens the longer the money stays put:
| Time | Simple interest | Compounded monthly | Difference |
|---|---|---|---|
| 1 year | $10,500 | $10,512 | $12 |
| 2 years | $11,000 | $11,049 | $49 |
| 5 years | $12,500 | $12,834 | $334 |
| 10 years | $15,000 | $16,470 | $1,470 |
| 20 years | $20,000 | $27,126 | $7,126 |
| 30 years | $25,000 | $44,677 | $19,677 |
For multi-year savings or investments, see the compound interest calculator or the savings calculator.
Simple interest on $10,000
| Annual rate | 1 year | 3 years | 5 years | 10 years |
|---|---|---|---|---|
| 3% | $300 | $900 | $1,500 | $3,000 |
| 5% | $500 | $1,500 | $2,500 | $5,000 |
| 7% | $700 | $2,100 | $3,500 | $7,000 |
| 10% | $1,000 | $3,000 | $5,000 | $10,000 |
Where simple interest is used
- Auto loans. According to the CFPB, simple interest is the more common method on car loans: interest is calculated daily or monthly on your actual outstanding balance. Each payment covers the interest accrued since the last one, and the rest reduces the balance, so extra or early payments save interest. Estimate payments with the auto loan calculator.
- Treasury bills. T-bills pay no periodic interest. They are sold at a discount and pay face value at maturity, and TreasuryDirect prices them with a simple-interest style discount on a 360-day year: Price = Face value × (1 − discount rate × days ÷ 360). In TreasuryDirect’s example, a $1,000 26-week bill at a 0.145% discount rate for 182 days sells for $999.27, a discount of $0.73.
- Short-term and interest-only arrangements. When interest is paid out rather than added to the balance, as with some CDs that pay interest by check or transfer, the balance does not compound and I = P × r × t describes the interest for each period.
Frequently asked questions
How do you calculate simple interest?
Multiply the principal by the annual interest rate (as a decimal) and by the time in years: I = P × r × t. For $10,000 at 5% for 3 years, I = $10,000 × 0.05 × 3 = $1,500. Add the interest to the principal to get the total amount, $11,500. Convert months to years by dividing by 12 and days by dividing by 365 or 360.
What is the difference between simple and compound interest?
Simple interest is paid only on the original principal, so it grows by the same dollar amount each year. Compound interest is also paid on interest already earned, so growth speeds up over time. On $10,000 at 5%, simple interest totals $25,000 after 30 years, while monthly compounding reaches $44,677.
How do I find the principal, rate or time?
Rearrange I = P × r × t. Principal: P = I ÷ (r × t). Rate: r = I ÷ (P × t). Time: t = I ÷ (P × r). For example, earning $450 on $5,000 at 6% takes t = 450 ÷ (5,000 × 0.06) = 1.5 years. Choose the “Solve for” option in the calculator to do the rearranging for you.
Should I use 365 or 360 days in a year?
Use the convention in your loan or investment documents. A 365-day year counts actual days; a 360-day year, sometimes called the banker’s year, divides the annual rate by 360, which produces slightly more interest per day. For $10,000 at 6% for 90 days, that is $147.95 with 365 days versus $150.00 with 360. Treasury bill pricing uses 360.
Are car loans simple interest?
Many are. The CFPB says simple interest is the more common method on auto loans: interest is figured daily or monthly on the balance you still owe, so extra payments reduce what you owe and paying off early saves interest. The alternative, precomputed interest, adds the interest to the loan up front, and extra payments do not reduce it. Check your contract to see which one applies.
Do savings accounts pay simple interest?
Usually not over time. Banks calculate deposit interest daily, and once interest is credited to the account it earns interest too, which is compounding. That is why savings accounts and CDs quote an APY, which includes the effect of compounding. Simple interest is a good description of short loans, interest-only arrangements and investments that pay interest out instead of reinvesting it.