## What is a 'Stated Annual Interest Rate'

A stated annual interest rate is the return on an investment (ROI) that is expressed as a per-year percentage. It does not account for compounding that occurs throughout the year. The effective annual interest rate, on the other hand, does account for intra-year compounding, which can occur on a daily, monthly or quarterly basis. Typically, the effective annual interest rate will lead to higher returns than the stated annual interest rate due to the power of compounding. Investors can compare products and calculate which type of interest will offer the most favorable return.

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## BREAKING DOWN '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 certificate of deposit.

## Stated Annual Interest Rate and Compound Interest

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 is:

Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value)

= [P (1 + i) n] – P

= P [(1 + i) n – 1]

(Where P = Principal, i = nominal annual interest rate in percentage terms, and n = number of compounding periods.)

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 4% 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.

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