Understanding and Calculating the Stated Annual Interest Rate

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 occurs throughout the year. Effective annual interest rate” (EAR) takes compounding into account and is often higher. Banks may use SAR to make loan rates appear lower. It is important for consumers and investors to understand the difference between SAR and EAR to make informed financial decisions.

How the Stated Annual Interest Rate Works

The stated annual return is the 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 effective annual interest rate, or EAR, this interest rate does not take the effect of compound interest into account.

On Loans

When banks charge interest, the stated interest rate is often used instead of the effective annual interest rate to make consumers believe that they are getting a lower interest rate than they actually will pay.

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 stated interest rate instead of the effective interest rate.

On Investments

For the interest a bank pays on a deposit account, 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 annual interest rate of 10.47% rather than the stated interest rate of 10%.

Comparing Stated and Effective Annual Interest Rates

The stated annual interest rate results in a straightforward amount 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 do not compound interest, the stated rate and the effective rate are the same.

Investors can compare products and calculate which type of interest 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.

Real-World Example of a Stated Annual Interest Rate

A $10,000, one-year certificate of deposit (CD) with 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 savings account that paid 10% and compounded 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 interest earned would be $1,047.13. The account value at that time will be $11,047.13. The effective annual interest 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 simple interest associated with a stated annual rate involving no compounding interest.

Steps to Calculate Stated Annual Rate in Excel

Microsoft Excel is a common tool used to calculate compound interest. One way to calculate it is to multiply each year’s new balance by the interest rate. For example, suppose you deposit $1,000 into a savings account with a 5% interest rate that compounds annually and you want to calculate your balance after five years. You would calculate it by following these steps:

1. Enter “Year” in cell A1 and “Balance” in cell B1.
2. Input years 0 to 5 in cells A2 through A7.
3. Start with “1000” in cell B2, representing the initial principal.
4. Use the formula “=B2*1.05” in cell B3 to compute the balance for year 1.
5. Continue using the format “=B3*1.05” in successive cells up to B7.
6. Calculate the interest balance in cell B7 (after five years).
7. Subtract the initial amount from this balance to determine the compound interest earned.

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. This contrasts with the effective annual interest rate, which accounts for compounding, making it typically higher.