A Web site for E*TRADE Financial claims that they have "one...

A Web site for E*TRADE Financial claims that they have "one of the highest yields in the nation" on a 6 -month CD. The stated yield was $5.46 \% ;$ the actual rate was not stated. Assuming monthly compounding, find the actual rate. Source: $E^{*}$TRADE .

Key Concepts

Compound Interest

Compound interest is the process where the interest earned is reinvested to earn additional interest over time, meaning interest is earned on both the original principal and the accumulated interest from previous periods. This concept is fundamental in financial calculations involving investments and loans, as it illustrates how money grows at an accelerating rate based on the frequency of compounding.

Effective Annual Rate

The effective annual rate (EAR) represents the actual annual yield or cost of an investment or loan after accounting for the effects of compounding over a year. It is calculated using the formula EAR = (1 + (nominal rate/number of compounding periods))^(number of periods) - 1, which converts a nominal annual interest rate into the effective rate that truly reflects the compounded return.

Nominal Interest Rate

The nominal interest rate is the stated or advertised rate of interest that does not consider the effects of compounding within the year. It is often used as a baseline figure, but without accounting for the frequency of compounding, it does not accurately represent the actual rate of return or cost when compared to the effective annual rate.

Compounding Frequency

Compounding frequency refers to the number of times per year that interest is calculated and added to the balance. The frequency of compounding (e.g., monthly, quarterly, annually) directly affects the amount of interest accrued, with more frequent compounding leading to a higher effective yield even when the nominal rate remains unchanged.

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