What Is the Stated Annual Interest Rate?
The stated annual interest rate, sometimes referred to as SAR, is the return on an investment (ROI) 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.
- 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.
- Banks will often show whichever rate appears more favorable, according to the financial product they're selling.
Understanding the Stated Annual Interest Rate
The stated annual return is the simple annual return that a bank gives you on a loan. Unlike the effective annual interest rate, or EAR, this interest rate does not take the effect of compound interest into account.
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 paying a lower interest rate. For example, for a loan at a stated interest rate of 30%, compounded monthly, the effective annual interest rate would be 34.48%. In such scenarios, banks will typically advertise the stated interest rate instead of the effective interest rate.
For the interest a bank pays on a deposit account, the effective annual rate is advertised because it looks more attractive. For example, for a deposit at a stated rate of 10% compounded monthly, the effective annual interest rate would be 10.47%. Banks will advertise the effective annual interest rate of 10.47% rather than the stated interest rate of 10%.
Stated Annual Interest Rate vs. Effective Annual Interest Rate
The effective annual interest rate accounts for intra-year compounding, which can occur on a daily, monthly, or quarterly basis. The more frequently compounding occurs, the higher the effective interest rate and the difference between 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 will offer the most favorable return. Typically, the effective annual interest rate will be higher than the stated annual interest rate due to the power of compounding.
The effective annual rate is a key tool for evaluating the true return on an investment or the true interest rate on a loan and is often used for figuring out the best financial strategies for people or organizations.
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.
If the money was placed in an interest-earning savings account that paid 10% compounded monthly, the account will earn interest at a rate of 0.833% each month (10% divided by 12 months; 10/12 = 0.833). Over the course of the year, this account will earn $1,047.13 in interest, at an effective annual interest rate of 10.47%, which is notably higher than the returns on the 10% stated annual interest rate of the CD.
Calculating the Effective Annual Rate
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 simple interest or going with a stated annual rate—as this is only calculated on the principal amount as stated above.
The exact formula for calculating compound interest on the effective annual rate is:
(Where i = nominal annual interest rate in percentage terms, and n = number of compounding periods.)
Calculating SAR and EAR in Excel
Excel is a common tool for calculating compound interest. One method 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 the balance in five years.
On Microsoft Excel, enter "Year" into cell A1 and "Balance" into cell B1. Enter years 0 to 5 into cells A2 through A7. The balance for year 0 is $1,000, so you would enter "1000" into cell B2. Next, enter "=B2*1.05" into cell B3. Then enter "=B3*1.05" into cell B4 and continue to do this until you get to cell B7. In cell B7, the calculation is "=B6*1.05."
Finally, the calculated value in cell B7, $1,216.65, is the balance in your savings account after five years. To find the compound interest value, subtract $1,000 from $1,216.65; this gives you a value of $216.65.