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Stated Annual Interest Rate: What It Is and How to Calculate It

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Updated April 22, 2021

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What Is the Stated Annual Interest Rate?

The stated annual interest rate, sometimes referred to as SAR, is the return on an investment (ROI) or the rate charged on a loan that is expressed as a per-year percentage. It is a simple interest rate calculation that does not account for any compounding that occ𒁏urs throughout the year.

Key Takeaways

The stated annual rate describes an annualized rate of interest that does not take into account the effect of intra-year compounding.
Effective annual rates do account for intra-year compounding of interest.
Stated annual rates are lower than effective annual rates due to their lack of compound interest.
Banks will often highlight the rate that is more likely to attract customers.
Stated rates can be more appealing to loan shoppers while effective rates are more so for investors.

Understanding the Stated Annual Interest Rate

The stated annual return is the 澳洲幸运5官方开奖结果体彩网:simple interest annual return that a bank charges you for a loan or that you receive on a deposit account or an investment. Unlike the 澳洲幸运5官方开奖结果体彩网:effective annual interest rate, or EAR, this 澳洲幸运5官方开奖结果体彩网:interest rate does not ౠtake the effect of compound interest into account.

On Loans

When banks charge interest, the stated interest rate is often used in🐓stead of the effective annual interest rate to make consumers believe that they are getting a lower interest rate than they actually will pa🔥y.

For example, a loan with a stated interest 😼rate of 30%, compounded monthly, would have an effective annual interest rate of 34.48%. In such scenarios, banks will typically advertise the lower stat▨ed interest rate instead of the effective interest rate.

On Investments

For the interest a bank pays on a deposit accouಌnt, the effective annual rate is advertised because it looks more attractive.

For example, a deposit account with a stated rate of 10% compounded monthly would have an effective annual interest rate of 10.47%. In this case, banks will advertise the effective ꩲannual interest rate of 10.47% rather than the stated interest rate of 10%.

Stated Annual Interest Rate vs. Effective Ann😼ual Interest Rate

The stated annual interest rate results in a straightforward amouဣnt of annual interest obtained by simply multiplying the stated rate by the principal amount.

The effective annual interest rate accounts for intra-year compounding, which can occur on a daily, monthly, or quarterly basis. As it's earned, each interest amount is added to the principal and subsequent earnings are calculated on increasingly higher principal plus interest amounts.

The more frequently compounding occurs, the higher the effective interest rate and the greater the difference between it and the stated interest rate will be. For loans that doꦑ not compound intereꦇst, the stated rate and the effective rate are the same.

Investors can compare products and calculate which type of intere🎃st 🅠rate will offer the more favorable return. Typically, the effective annual interest rate will be higher than the stated annual interest rate due to the power of compounding.

Important

The effective annual rate is a key tool used to evaluate the true return on an investment or the true interest rate on a loan. It is often used to determine the best financial strategies for people or or🍰ganizations.

Example of a Stated Annual Interest Rate

A $10,000, one-year certificate of deposit (CD) wit🎀h a stated ▨annual interest rate of 10% will earn $1,000 at maturity. The account value at that time will be $11,000.

The formula used to calculate the interest amount is:

Principal x Rate of Interest, or $10,000 x .10 = $1,000

If $10,000 were placed in an interest-earning 澳洲幸运5官方开奖结果体彩网:savings account that paid 10% and compou🔯nded monthly, the account would earn interest at a rate of 0.833% each 🍷month (10%/12 months = 0.833).

By the end of the year, the total inꦅterest earned would be $1,047.13. The account value at that time will be $11,047.13. The effective annual intere꧅st rate would be 10.47%, which is notably higher than the return on the 10% stated annual interest rate CD.

Formula for the Effective Annual Rate

The formula used to calculate the effective annual interest rate is:

(1 + i/n) ⁿ – 1

where i = the stated annual interest rate and n = the number of compounding periods.

Compound interest is one of the fundamental principles of finance. The concept is said to have originated in 17th-century Italy. Often described as interest on interest, compound interest makes a sum grow at a faster rate than the s🌳imple interest associated with a sta𒁃ted annual rate involving no compounding interest.

Calculating SAR in Excel

Microsoft Excel is a common tool used to calculate compound interest. One way to calculate it is to multiply each year's 澳洲幸运5官方开奖结果体彩网:new balance by the interest rate. For example, suppose you deposit $1,000 into a savings account with a 5% interest rate tha⛦t compounds annually and you want to calculate your balance after five years.

In Excel, enter "Year" in cell A1 and "Balance" in cell B1. Enter years 0 to 5 in cells A2 through A7. The balance for year 0 is $1,000, so enter "1000" in cell B2. Next, enter "=B2*1.05" in cell B3. Then enter "=B3*1.05" in cell B4 and continue to do this until you get to cell B7. In cell B7, the calculation is "=B6*1.05."

The calculated value in cell B7, $1,216.65, is the balance in your savi♈ngs account after five years. To find the compound interest value, subtract $1,000 from $1,216.65 for a value of $216.65.

Is the Stated Interest Rate More Than the Effective Interest Rate?

Due to the addition of compounding interest over time to the principal, the effective interest rate is normally higher. The stated interest rate doesn't include compound interest.

What's Another Name for the Stated Annual Interest Rate?

When dealing with investments, you may see the stated annual interest rate referred to as a cou▨pon rate or face interඣest rate.

Why Is Compound Interest Important to Investors?

It's very important because it can make your account balance grow faster than interest that doesn't compound. That's because over time, interest is calculated on an increasing amount of interest plus principal.

The Bottom Line

The stated annual interest rate is the interest rate on a loan, bank deposit, or investment that's calculated as simple interest. It doesn't take into account any compounding of interest.

It's often contrasted with the effective annual interest rate. This is normally a higher interest rate due to the compounding interest that's part of its calculation.

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