# How to Calculate Simple Interest: Math Calculations

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Simple interest calculations aren’t as hard as they look – especially if you know what the variables stand for, and how the terms are defined. Click for larger view. Image by Decoded Science.

Learning how to calculate simple interest starts with knowing how to multiply. Why does this financial tool seem so mysterious?

## What is Simple Interest? What is Compound Interest?

There is a huge difference between simple interest and compound interest. To calculate interest of either type, you multiply a principal amount (the amount on which you’re paying or earning interest) by the interest rate; the difference lies in the principal. Simple interest excludes any prior interest amount from the principal; but compound interest includes earned interest in the principal.

## Including Fees in a Simple Interest Calculation

Sometimes you need to calculate other values besides the interest amount for a loan using simple interest calculations.

One example is a “late payment fee.” Some companies will charge a percentage of the outstanding balance as a fee for late payments. Some jurisdictions choose to consider this late payment fee as a simple interest charge, which may exceed the allowable annual interest rate.

• Use the formula r=I/(P*t) to calculate the rate of interest based on Interest amount divided by the product of Principal multiplied by the amount of time.

For example, a 1% late payment fee on a \$100 balance is \$1.00. If the balance is paid 10 days late, the effective annual interest rate is 1% in 10/365 of a year. So the calculation is:

• r=I/(P*t)=(\$1)/((\$100)*(10/365))=365/1000=.365=36.50%.

The company charged an effective interest rate of 36.5%.

The same reasoning applies to “pay day loans.”

## All Variations on the Simple Interest Rate Formula

We can summarize the variations on the simple interest rate formula as:

• I=P*r*t, to calculate the Interest Amount.
• r=I/(P*t), to calculate the effective interest rate.
• P=I/(r*t), to calculate the Principal.
• t=I/(P*r), to calculate the time period.
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