# Simple Interest Calculator

Starting Amount (PV)?:
Annual Interest Rate?:
Number of Days? (#):
Start Date? (m/d/y):
//
End Date? (m/d/y):
//
Days In Year?:

Interest Earned:
Future Value (FV):
Annual Percentage Yield (APY):
Daily Interest Rate?:

Enter an amount and a nominal annual interest rate.

Date Math: If you change either date, the number of days between the two dates will be calculated. If you enter a positive number of days, the end date will be updated. If you enter a negative number of days the start date will be updated. But note, a start date set to January 1st and an end date set to January 1st is not one day. It is 0 days. A day is 24 hours. Thus one day is January 1st to January 2nd.

The above means you can calculate interest for a specific number of days and not worry about what the dates are. If you need to know the interest for 31 days, then enter 31 for the number of days and don't worry about the dates.

Set the days in year. If you don't know, use a 365 day year. Click "Calc". The interest will be calculated for the exact number of days. Additionally, the future value is calculated (FV is the starting amount (PV) plus the interest.) The annual percentage yield is used for comparing investments. It is the rate institutions must quote in the US for interest bearing accounts. The holder of such an account can use the APY to compare accounts.

Interest may be calculated based on a unit of time, say a month. In that case, a month's interest is always the same for the same interest rate and same principal balance regardless of the length of the month. Given \$10,000 principal and an interest rate of 6.75% the interest will be the same for February as it will be March.

There is also exact day interest. Interest is calculated based on the exact number of days. This calculator calculates exact day interest and the future value.

Styles:

plain
plainer
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Currency
\$1,234.56
\$1.234,56
£1,234.56
1,234.56
Conventions:
€1,234.56
€1.234,56
1 234,56 €
1.234,56 €
Click on desired currency convention or style to change.

This calculator calculates the simple interest earned between any two dates. You can also use it as a date math calculator.

Simple interest calculations require that interest not be calculated on the interest earned during prior periods. Interest is only calculated on the original amount invested or borrowed. This contrasts with compound interest calculations where interest is calculated on the interest earned in prior periods. (See our online compound interest calculator for details about how compound interest is calculated.)

The amount that you start with is known as the present value (PV). The calculator adds the interest earned to the PV to arrive at the future value (FV).

Please click on the above "Help" button for details about using the calculator.

If you would like to know the interest earned on a series of deposits then use our future value calculator for Windows which is found in SolveIT!.

## How Simple Interest is Calculated

To understand simple interest, it is helpful to first understand the concept of a unit period. For the purpose of this discussion, a period is a consistent unit of time. That is, a period may be a day, a week, a month a year, or any other unit of time that is consistent over the entire term for which money is borrowed or invested. The term, that is the time between the start date and end date is divided up into the selected unit periods.

Interest is normally calculated as of the end or each period.

Our simple interest calculator calculates interest for the exact number of days. Therefore, this calculator's unit period is one day.

## Simple Interest Equation

This is the formula for simple interest calculations:

Simple Interest = Amt * Rate * Periods

Amt is the principal amount as of the start date. In financial jargon the Amt is the present value (or PV).

Rate is the periodic interest rate expressed as a decimal value. The periodic rate is calculated by the dividing the quoted annual interest rate by the number of periods in a year.

As already mentioned, this calculator uses the "day" as the unit period. This leads to an anomaly. Normally one would think that there are 365 days in a year except for leap years. However, our banker friends long ago (before computers were common) came up with another count for the days in the year. Because debts are frequently paid monthly, it was much easier to standardize on a 30 day month thus making interest for all months the same. This meant that a year was 360 days long (12 months * 30). So, the days in year is 360. In other words the rate in the above formula would be calculate by taking the annual interest rate divided by 360. This little twist also happens to increase the interest amount. Clever. Note that our simple interest calculator supports 360, 364 and 365 day years. (The 364 day year derives from 52, 7 day weeks in a year, or 364.)

Periods is the number of periods over the entire term. Term is the time from start date to end date inclusive.

## A simple (sorry) example of simple interest.

Assume \$10,000 is invested for one year at a 10% annual interest rate. Using the above formula and a 365 day year, we see that the interest earned for one year is \$1,000.00.

\$1,000 = \$10,000 * (10.0/100/365) * 365

Next assume one more full year has passed and that the amount has not changed either due to a loan payment or a deposit or withdrawal. The interest earned for the second year will again be \$1,000.00, still 10.0% of the original \$10,000 investment or loan amount. And after two years the balance is \$10,000 + \$1,000 + \$1,000 or a total of 12,000.00.

Exercise: Calculate the interest on \$10,000 for one year but this time using a 360 day year. Does the interest amount go up or down? By how much?

What's the practical benefit of knowing this? Well, if you are a borrower, then at any given interest rate, simple interest loans are to your advantage. If you are an investor, then all other things being equal, earning simple interest is a disadvantage.

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