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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