Simple Interest Calculator

What this calculator answers

How much interest a principal earns or costs at a flat annual rate over a set time, and the total at the end. Simple interest is charged on the original principal only, so the same amount accrues every year. Turned around, it also answers the reverse questions: the principal needed to reach a total, the rate that turns one amount into another, and how long a sum takes to earn a given amount. It fits short-term loans repaid in one payment, certificates of deposit that pay simple interest, any agreement that states interest on the original amount, and I = Prt problems in class.

How to use it

• Find: what you want to work out. Interest and total is the usual case; choose principal, interest rate or time to solve for that instead.
• Principal: the amount deposited or borrowed, in dollars. 10,000, $10,000 and 10k all work.
• Annual interest rate: the yearly rate in percent. Type 5 for 5%, not 0.05. 0% is allowed, except when finding the time or finding the principal from the interest.
• Time and time unit: how long the money is lent or invested, in years, months or days. Days must be whole days. When you find the time, the unit sets how the answer is shown.
• Days in a year (shown for days only): 365 or 360. Use the one in your agreement (see below).
• Amount you know (when finding the principal, rate or time): the total at the end (principal plus interest) or the interest alone, in dollars.

Results update as you type. When the time is a year or longer, a year-by-year table appears, which you can download as a CSV file, and a chart compares the balance with the same rate compounded once a year. The Try buttons load the cases worked through below: 18 months, 90 days on a 360-day year, 30 years, and two reverse questions. To weigh two offers, press Save for comparison, change the inputs and save again: each saved scenario shows how much its interest and total differ from the first. If the money is a loan you will repay in installments, Continue in the Loan Payment Calculator takes the principal, rate and time over to work out the payment.

How to calculate simple interest (I = Prt)

Multiply the principal by the annual rate as a decimal and by the time in years. Add the interest to the principal for the total.

$$I = P \times r \times t \qquad A = P + I = P\,(1 + r\,t)$$

• $I$ is the interest, in dollars.
• $P$ is the principal.
• $r$ is the annual rate as a decimal (5% is 0.05).
• $t$ is the time in years: months ÷ 12, or days ÷ 365 (or 360).
• $A$ is the total: principal plus interest.

Worked example: $10,000 at 5% for 3 years

1. Rate as a decimal: r = 5 ÷ 100 = 0.05.
2. Interest: I = $10,000 × 0.05 × 3 = $1,500.00.
3. Total: A = $10,000 + $1,500.00 = $11,500.00.

The interest is $500.00 every year, so the year-end totals are $10,500.00, $11,000.00 and $11,500.00. Compounded once a year at the same rate, the same money would grow to $11,576.25, which is $76.25 more, because each year’s interest would earn interest too.

Simple interest for months and days: 365 or 360?

Convert the time to years first. For months, divide by 12: eighteen months is 1.5 years, so $10,000 at 5% earns $10,000 × 0.05 × 1.5 = $750.00.

For days, divide by the number of days in a year. The textbook method divides by 365 (called Actual/365). U.S. money markets count the actual days but assume a 360-day year. If your agreement says 360, choose 360. Dividing by 360 gives 365 ÷ 360 ≈ 1.0139 times the interest for the same days, about 1.4% more:

If you know the start and end dates rather than the number of days, count the days between them first. Whether both the first and the last day count depends on your agreement.

How to find the principal, rate or time

Rearrange I = Prt for the value you don’t know. If you know the total rather than the interest, the interest is the total minus the principal, I = A − P.

• Principal: P = A ÷ (1 + r × t), or P = I ÷ (r × t) from the interest.
• Rate: r = I ÷ (P × t). Multiply by 100 for a percentage.
• Time: t = I ÷ (P × r), in years. Multiply by 12 for months, or by 365 (or 360) for days.

What rate turns $2,000 into $2,300 in 2 years? The interest is $2,300 − $2,000 = $300, so r = $300 ÷ ($2,000 × 2) = 0.075, or 7.5% a year.

How long does $5,000 take to earn $1,000 at 4%? t = $1,000 ÷ ($5,000 × 0.04) = 5 years.

How much must you deposit now to have $15,000 in 5 years at 6%? P = $15,000 ÷ (1 + 0.06 × 5) = $15,000 ÷ 1.3 = $11,538.46 to the nearest cent. The textbook rounds a deposit like this up to $11,538.47, because $11,538.46 grows to $14,999.998, just short of the goal.

The rate needs a total at least as large as the principal, and the time needs a rate above 0%. The calculator says so instead of showing a negative rate or an endless time.

Reading the result

• The headline is what you chose to find: the interest for the whole time, or the principal, rate or time.
• Total (or Interest, when you entered the total) completes the picture: what a saver has at the end, or what a borrower repays in one payment at the end.
• Interest per year is the flat rate at which interest builds up. Under it are the amounts per month (one-twelfth of a year’s interest, so 5% on $10,000 is $41.67 a month) and, when the time is in days, per day.
• Total if compounded yearly shows the same rate compounded once a year, for comparison only. For less than a year it comes out slightly lower than simple interest.
• The year-by-year table adds the same interest each full year. A part year at the end earns a matching share, and its row says so.
• The chart draws that balance as a straight line, next to a curve for the same rate compounded once a year. Its Chart data table lists every point.
• Interest at other rates repeats the calculation at 1 and 2 percentage points either side of your rate, with the same principal and time. Simple interest grows in a straight line with the rate, so every point adds the same amount: on $10,000 for 3 years, each point is $300.00, so 6% earns $1,800.00 where 5% earns $1,500.00. When you find the principal or the time, the table shows the principal or the time needed at those rates instead.

Simple vs. compound interest: what’s the difference?

Compound interest is paid on the principal and on interest already earned; simple interest never earns interest on interest. The gap grows with time and rate. Over 3 years at 5% it is $76.25 on $10,000. Over 30 years, simple interest brings $10,000 to $25,000.00, while yearly compounding brings it to $43,219.42.

Over more than a year, compounding at the same rate grows faster for a saver, and for a borrower simple interest on the original principal costs less than the same rate compounded. To project savings with regular deposits, use a compound interest calculator.

Assumptions and limitations

• Interest is earned on the original principal only, with no compounding.
• The rate stays the same for the whole time.
• There are no fees, taxes, deposits, withdrawals or payments during the term. A loan repaid in installments is not I = Prt on the original amount (see the questions below).
• Interest and balances are rounded to the cent only when displayed. The textbook practice is to round interest a borrower pays up to the next cent, and lenders may round each period’s interest their own way, so a statement can differ by a cent or more.
• The result is an educational estimate, not financial advice or a quote.

Common mistakes

• Typing the rate as a decimal. The rate field is in percent, so 0.05 means 0.05%, not 5%. The calculator points this out when you enter a small value like that.
• Using a monthly rate as the annual rate. If an agreement quotes 1.5% a month, the annual simple rate is 1.5% × 12 = 18%.
• Forgetting to convert months or days. t is in years: 6 months is 0.5, not 6.
• Using the wrong day count. 360 and 365 give different answers for the same days; check which one your agreement uses.
• Mixing up the total and the interest when solving. $2,300 at the end of a $2,000 loan is a total; the interest is $300. Choose which one you know before you type it.
• Using I = Prt for an installment loan. Each payment lowers the balance, so interest on the original amount overstates the cost. Use a loan payment calculator, which charges interest on the remaining balance, instead.