The seven-day yield and the Annual Percentage Yield both express annual returns on investment. Money-market funds report a seven-day yield because fund securities change frequently. The Truth in Savings Act sets forth the calculation of the APY, which is used to indicate the return for savings accounts, checking accounts and certificates of deposit.
Annual Percentage Yield
The APY formula is 100 times ((1 plus r) raised to the power of p minus 1), where "r" is the periodic rate and "p" is the number of periods. For example, if a savings account pays interest monthly at a periodic rate of 0.1 percent per month, the APY is 100 times ((1 plus 0.001) raised to the power of 12 minus 1), or 1.207 percent.
The seven-day yield is the annualized income generated over a seven-day period. According to Investing Answers, the formula is 100 times ((F minus B minus M) divided by B) times (365 divided by 7), where "F" is the value of the account at the end of a seven-day period, "B" is the value of the account at the start of the period and "M" is a week's worth of management fees and expenses. This formula assumes that the return on any seven-day period is the same throughout the year.
For example, if the seven-day starting and ending values of an account are $1,000 and $1,001.25, respectively, and the pro-rated fees are $0.25, then the annualized seven-day yield is 100 times (($1,001.25 minus $1,000 minus $0.25) divided by $1,000) times (365 divided by 7), which simplifies to 100 times ($1 divided by $1,000) times (365 divided by 7) or 5.21 percent. The seven-day effective yield would be higher because it includes compounding.
The Truth in Savings Act's legislative approach helps consumers compare between different investments, such as savings accounts and certificates of deposit, or savings accounts at different banks. Investors can use the seven-day yield to compare money market fund returns. Money-market funds registered with the U.S. Securities and Exchange Commission are required to hold low-risk short-term securities, such as certificates of deposit, Treasury bills and other liquid assets.
Considerations: APR vs. APY
APY is not the same as APR, which is the annual percentage rate on loans. Unlike APY, there is no compounding in APR. The periodic rate is multiplied by the number of periods. For example, 5 percent APR financing on a $20,000 car loan means monthly interest payments of about $83.30 ($20,000 times 0.05 divided by 12). Similarly, a daily credit card rate of 0.04 percent translates to an annual rate of 14.6 percent (0.04 times 365).