This lesson will provide the formula for how to calculate interest expense. This lesson will also explain the phrase and provide a sample calculation.

## Understanding Interest Expense

Roberta operates a car detailing business. Unfortunately for Roberta, one of her more expensive machines has recently stopped working. With very little savings, Roberta is contemplating purchasing a new machine with bank financing. That is, she wants to borrow money from a bank to purchase the machine.

Roberta meets with a loan officer from State Bank, who explains to her that interest expense is calculated in one of two ways. **Interest expense** can easily be explained as *the cost of borrowing money* or what the bank charges her to borrow the money.

Roberta has decided on a machine with a retail price of $18,290. Since she has already signed loan paperwork, the company sales desk agrees to sell her the machine for $17,000, including all taxes and fees.

Roberta returns to the bank and meets again with the loan officer. He arranges for the check to be sent to the sales desk and begins to explain to Roberta the two types of interest expense formulas.

## Simple Interest Expense

The loan officer, Randy, explains that when calculating interest expense, there are three variables: principal, rate, and time. He explains that one way to calculate interest expense is to use the simple interest expense formula. The **simple interest expense formula** excludes compounding. In other words, interest is not added to the principal. Let’s take a look at this formula.

**Interest Expense = Principal * Rate * Time**

So, if the bank used this formula and Roberta borrowed $17,000 over 5 years at 3%, her total interest expense would be $2,550. Calculating like this:

*Interest Expense = $17,000 * 3% * 5*

*Interest Expense = $17,000 * .15*

*Interest Expense = $2,550*

So, over the life of the loan, Roberta would repay $19,550.

## Compound Interest Expense

The **compound interest expense formula** includes compounding. Opposite the simple interest expense formula, the compound interest expense formula has interest accumulating on the unpaid principal. Randy explains: this is how the bank calculates the interest Roberta will pay over the life of her loan. Using this formula, Roberta stands to pay $2,747 in interest to the bank over the life of her loan. It is calculated like this:

**Interest Expense = (Principal * (1+ (R / N)) ^ (N * T)) – Principal**

Where: R = interest rate, N = number of times interest is compounded in a year, and T = time in years

*Interest Expense = ($17,000 * (1+ (3%/12)) ^ (12 * 5)) – $17,000*

*Interest Expense = ($17,000 * (1+.25%) ^ 60) – $17,000*

*Interest Expense = ($17,000 * 1.1616) – $17,000*

*Interest Expense = $19,747 – $17,000*

*Interest Expense = $2,747*

So, Roberta will pay more under the compound interest expense formula, since she will owe the bank $19,747.

## Lesson Summary

Let’s review. Roberta learned from a recent encounter with a bank when buying a new machine for her car detailing business, that there are two types of interest expense formulas: the simple interest expense formula and the compound interest expense formula.

Roberta’s bank uses the **compound interest expense formula**, in which interest accrues on the unpaid principle and looks like this:

*Interest Expense = (Principal * (1+ (R / N)) ^ (N * T)) – Principal*

The other interest expense formula is the **simple interest expense formula**, which does not compound interest. That formula is:

*Interest Expense = Principal * Rate * Time*.

Further, through the examples shown, it was determined that Roberta would pay more interest if her bank uses the compound interest expense formula. Roberta makes notes in the business files that in the future she should always ask the bank which type of interest expense they will use.