Simple Interest Definition: Who Benefits, With Formula and Example

Simple Interest

Investopedia / Nez Riaz

What Is Simple Interest?

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

This type of interest usually applies to automobile loans or short-term loans, although some mortgages use this calculation method.

Key Takeaways

  • Simple interest is calculated by multiplying the daily interest rate by the principal, by the number of days that elapse between payments.
  • Simple interest benefits consumers who pay their loans on time or early each month.
  • Auto loans and short-term personal loans are usually simple interest loans.

Understanding Simple Interest

Understanding Simple Interest

Interest is the cost of borrowing money. Typically expressed as a percentage, it amounts to a fee or extra charge the borrower pays the lender for the financed sum.

When you make a payment on a simple interest loan, the payment first goes toward that month’s interest, and the remainder goes toward the principal. Each month’s interest is paid in full so it never accrues. In contrast, compound interest adds some of the monthly interest back onto the loan; in each succeeding month, you pay new interest on old interest.

To understand how simple interest works, consider an automobile loan that has a $15,000 principal balance and an annual 5% simple interest rate. If your payment is due on May 1 and you pay it precisely on the due date, the finance company calculates your interest on the 30 days in April. Your interest for 30 days is $61.64 under this scenario. However, if you make the payment on April 21, the finance company charges you interest for only 20 days in April, dropping your interest payment to $41.09, a $20 savings.

Simple Interest Formula and Example

The formula for simple interest is pretty, well, simple. It looks like this:

Simple Interest = P × I × N where: P = Principal I = Daily interest rate N = Number of days between payments \begin{aligned}&\text{Simple Interest} = P \times I \times N\\&\textbf{where:}\\&P = \text{Principal}\\&I = \text{Daily interest rate} \\&N = \text{Number of days between payments}\end{aligned} Simple Interest=P×I×Nwhere:P=PrincipalI=Daily interest rateN=Number of days between payments

Generally, simple interest paid or received over a certain period is a fixed percentage of the principal amount that was borrowed or lent. For example, say a student obtains a simple-interest loan to pay one year of college tuition, which costs $18,000, and the annual interest rate on the loan is 6%. The student repays the loan over three years. The amount of simple interest paid is:

$ 3 , 240 = $ 18 , 000 × 0.06 × 3 \begin{aligned} &\$3,240 = \$18,000 \times 0.06 \times 3 \\ \end{aligned} $3,240=$18,000×0.06×3

and the total amount paid is:

$ 21 , 240 = $ 18 , 000 + $ 3 , 240 \begin{aligned} &\$21,240 = \$18,000 + \$3,240 \\ \end{aligned} $21,240=$18,000+$3,240

Who Benefits From a Simple Interest Loan?

Because simple interest is often calculated on a daily basis, it mostly benefits consumers who pay their bills or loans on time or early each month.

Under the student-loan scenario above, if you sent a $300 payment on May 1, then $238.36 goes toward the principal. If you sent the same payment on April 20, then $258.91 goes toward the principal. If you can pay early every month, your principal balance shrinks faster, and you pay the loan off sooner than the original estimate.

Conversely, if you pay the loan late, more of your payment goes toward interest than if you pay on time. Using the same automobile loan example, if your payment is due on May 1 and you make it on May 16, you get charged for 45 days of interest at a cost of $92.46. This means only $207.54 of your $300 payment goes toward the principal. If you consistently pay late over the life of a loan, your final payment will be larger than the original estimate because you did not pay down the principal at the expected rate.

What Types of Loans Use Simple Interest?

Simple interest usually applies to automobile loans or short-term personal loans. In the U.S., most mortgages on an amortization schedule are also simple interest loans, although they can certainly feel like compound interest ones.

The compounding feel comes from varying principal payments—that is, the percentage of your mortgage payment that's actually going towards the loan itself, not the interest. The interest doesn’t compound; the principal payments do. A $1,000 principal payment saves interest on that $1,000 and results in higher principal payments the next year, and higher the following year, and so on. If you don’t let the principal payments vary, as in an interest-only loan (zero principal payment), or by equalizing the principal payments, the loan interest itself doesn’t compound. Lowering the interest rate, shortening the loan term, or pre-paying principal also has a compounding effect.

For example, take bi-weekly mortgage payment plans. Bi-weekly plans generally help consumers pay off their mortgages early because the borrowers make two extra payments a year, saving interest over the life of the loan by paying off the principal faster.

If you're looking to take out a short-term personal loan, then a personal loan calculator can be a great tool for determining in advance an interest rate that's within your means.

Simple Interest vs. Compound Interest

Interest can be either simple or compounded. Simple interest is based on the original principal amount of a loan or deposit.

Compound interest, on the other hand, is based on the principal amount and the interest that accumulates on it in every period. Simple interest is calculated only on the principal, so it is easier to determine than compound interest.

In real-life situations, compound interest is often a factor in business transactions, investments, and financial products intended to extend for multiple periods or years. Simple interest is mainly used for easy calculations: those generally for a single period or less than a year. Simple interest also applies to open-ended situations, such as credit card balances.

Why is Simple Interest "Simple"?

"Simple" interest refers to the straightforward crediting of cash flows associated with some investment or deposit. For instance, 1% annual simple interest would credit $1 for every $100 invested, year after year. Simple interest does not, however, take into account the power of compounding, or interest-on-interest, where after the first year the 1% would actually be earned on the $101 balance—adding up to $1.01. The next year, the 1% would be earned on $102.01, amounting to $1.02. And so one.

Which Will Pay Out More Over Time, Simple or Compound Interest?

Compound interest will always pay more after the first payment period. Suppose you borrow $10,000 at a 10% annual interest rate with the principal and interest due as a lump sum in three years. Using a simple interest calculation, 10% of the principal balance gets added to your repayment amount during each of the three years. That comes out to $1,000 per year, which totals $3,000 in interest over the life of the loan. At repayment, then, the amount due is $13,000. Now suppose you take out the same loan, with the same terms, but the interest is compounded annually. When the loan is due, instead of owing $13,000, you end up owing $13,310. While you may not consider $310 a huge difference, this example is only a three-year loan; compound interest piles up and becomes oppressive with longer loan terms.

What Are Some Financial Instruments That Use Simple Interest?

Most coupon-paying bonds utilize simple interest. So do most personal loans, including student loans and auto loans, and home mortgages.

What Are Some Financial Instruments That Use Compound Interest?

Most bank deposit accounts, credit cards, and some lines of credit will tend to use compound interest.