What Is the Annual Percentage Yield (APY) and How Is It Calculated?
The annual percentage yield, almost always shortened to APY, is the standard figure that banks and savings institutions in the United States use to state what a deposit account pays. It exists because two accounts can quote the same interest rate and still pay different amounts: one may compound daily and another annually, one may run for six months and another for two years, and one may change its rate after an introductory period. The APY converts each of these arrangements into a single annualised percentage so that a consumer can set one account beside another.
The APY is a creature of federal law. The Truth in Savings Act of 1991, enacted as part of the Federal Deposit Insurance Corporation Improvement Act of 1991, requires it, and Regulation DD, codified at 12 CFR part 1030 and issued by the Consumer Financial Protection Bureau, sets out how it is computed, when it must be disclosed and how it may be advertised. Regulation DD states its own purpose as enabling consumers to make informed decisions about accounts at depository institutions and to make meaningful comparisons among those institutions. This article covers the definition, the appendix A formula, the interest-payment rules behind the figure, the disclosure and advertising rules, and the contrast with the loan APR under Regulation Z.
What the Annual Percentage Yield Measures
Regulation DD defines the annual percentage yield as a percentage rate reflecting the total amount of interest paid on an account, based on the interest rate and the frequency of compounding for a 365-day period, and calculated according to the rules in appendix A. The interest rate, by contrast, is defined as the annual rate of interest paid on an account which does not reflect compounding. The two figures therefore differ whenever interest is compounded within the year, and the APY is the one built to be compared.
Appendix A adds that the APY reflects only interest. It does not include the value of any bonus offered to open, maintain, increase or renew an account, and it leaves out interest or other earnings that depend on circumstances that may or may not occur in the future. Nothing in the formula deducts the account's fees: the inputs are the interest earned and the principal that earned it. That is why, as later sections explain, an advertisement that states an APY must separately warn that fees could reduce the earnings on the account.
One terminological point surprises many readers. For the account disclosures given when an account is opened, Regulation DD allows the interest rate to be referred to as the "annual percentage rate" in addition to being called the "interest rate". On a deposit account, then, an "annual percentage rate" so labelled is simply the uncompounded interest rate, not a separate cost measure of the kind used for loans.
Which Accounts and Institutions Truth in Savings Covers
Regulation DD applies to depository institutions other than credit unions. Its advertising rules reach further than the institutions themselves: they apply to any person who advertises an account offered by a depository institution, including deposit brokers.
The regulation protects consumers, defined as natural persons who hold an account primarily for personal, family or household purposes. The official interpretations draw the boundary with examples. Accounts held by individuals as sole proprietors are not covered, and neither are accounts held by a natural person for another in a professional capacity, such as attorney-client trust accounts and landlord-tenant security accounts. An account held by an individual for a child under the Uniform Gifts to Minors Act is covered, as are individual retirement accounts and SEP accounts to the extent their funds sit in covered accounts; Keogh accounts are not subject to the regulation.
Not every product a bank sells is an "account". The interpretations list government securities, mutual funds, annuities, securities or obligations of the depository institution itself, and contractual arrangements such as repurchase agreements and bankers acceptances as products outside the term. A consumer who buys a mutual fund through a bank's branch therefore receives no Regulation DD APY for it; the regulation's yield belongs to deposits, including time, demand, savings and negotiable order of withdrawal accounts.
The General Formula and the Days in the Term
Part I of appendix A gives one general formula for the APY used in account disclosures and advertisements. Expressed in words, the APY equals one hundred times the result of taking one plus the interest divided by the principal, raising it to the power of 365 divided by the days in the term, and subtracting one. Principal is the amount assumed to have been deposited at the beginning of the account, interest is the total dollars earned on that principal for the term, and the days in the term are the actual number of days the account runs.
When the term is exactly 365 days, or the account has no stated maturity and so takes an assumed 365-day term, the exponent is one and the formula collapses to a simple one: one hundred times interest divided by principal. A one-year certificate that pays 52.50 dollars on a 1,000 dollar deposit therefore has an APY of 5.25 percent.
For a shorter term the exponent is greater than one, so the term's return is treated as though it were earned again for the rest of the year. The appendix's own example is a six-month certificate whose six-month period contains 182 days and which pays 30.37 dollars on 1,000 dollars: the APY is 6.18 percent, more than double the 3.037 percent earned over the term itself.
For time accounts offered in multiples of months, an institution may count either the actual days in the period or the number of days that would occur for any actual sequence of that many calendar months. If it chooses the second approach, it must use the same number of days to calculate the dollar interest earned that it uses in the APY formula. The appendix also permits the APY to be calculated on a 365-day or a 366-day year in a leap year.
Variable-Rate Accounts and Introductory Rates
A variable-rate account is one in which the interest rate may change after the account is opened. For a variable-rate account without an introductory premium or discounted rate, appendix A requires the institution to base the calculation only on the initial interest rate in effect when the account is opened or advertised, and to assume that this rate will not change during the year.
An account with an introductory premium or discount rate is calculated like a stepped-rate account. The institution assumes the introductory rate is in effect for the period the deposit contract provides, and that for the remainder of the year the variable rate that would otherwise have applied is in effect. If the variable rate is tied to an index, the index-based rate in effect at the time of disclosure is used for the remainder of the year. If it is not tied to an index, the institution uses the rate in effect for existing consumers holding the same account who are not receiving the introductory rate.
The appendix's example is an account paying 7 percent, compounded daily, for an introductory 91 days, where the variable rate that would otherwise have applied is 5 percent. On 1,000 dollars, 91 days at 7 percent followed by 274 days at 5 percent produce 56.52 dollars of interest for the year, so the APY is 5.65 percent: a figure between the two rates, weighted towards the rate that runs for longer.
Rounding and the Accuracy Tolerance
Regulation DD requires the APY, the APY earned and the interest rate to be rounded to the nearest one-hundredth of one percentage point and expressed to two decimal places, although in account disclosures the interest rate may be stated to more decimal places. The official interpretations give the examples: an APY calculated at 5.644 percent may be disclosed as 5.64 percent, and one calculated at 5.645 percent is rounded up and disclosed as 5.65 percent.
The regulation then allows a margin for error. The APY and the APY earned are considered accurate if they are not more than one-twentieth of one percentage point, that is 0.05 percentage point, above or below the figure determined under appendix A. A disclosed APY of 5.12 percent where the correct figure is 5.16 percent is therefore treated as accurate, while a disclosed 5.09 percent against the same correct figure is not.
The interpretations explain what the margin is for. It is designed to accommodate inadvertent errors, and institutions may not purposely incorporate the tolerance into their calculation of yields. A bank that deliberately shades every APY down by four hundredths of a point has not made use of the tolerance; it has disclosed figures that do not follow appendix A.
Balance Computation Methods
The APY assumes interest is paid on the money actually in the account, and Regulation DD's payment-of-interest rule makes that assumption true. Institutions must calculate interest on the full amount of principal in an account for each day, using either the daily balance method, which applies a daily periodic rate to the full principal each day, or the average daily balance method, which applies a periodic rate to the average of the daily balances over the period.
The official interpretations name methods that fail this requirement: paying interest on the balance at the end of the period, the "ending balance" method; paying interest for the period on the lowest balance on any day in it, the "low balance" method; and paying interest on a percentage of the balance that excludes the amount set aside for reserve requirements, the "investable balance" method. Each would pay interest on less than the full principal for some days.
The rule also sets a floor on the daily rate. Institutions must use a daily rate of at least 1/365 of the interest rate, and may use 1/366 in a leap year. A larger daily rate, such as 1/360 of the interest rate, is permitted as long as it is applied 365 days a year, because the consumer then receives more than the stated rate rather than less.
Minimum Balances and the Full-Balance Rule
Many accounts pay interest only when the balance reaches a minimum. Regulation DD requires an institution to use the same method to determine any minimum balance required to earn interest as it uses to determine the balance on which interest is calculated. An institution on the daily balance method may decline to pay interest for the days when the balance falls below the minimum; one on the average daily balance method may decline to pay interest for the period in which the balance falls below it.
An institution may not require consumers to maintain both a minimum daily balance and a minimum average daily balance to earn interest. It may, however, add a second method that is unequivocally beneficial to the consumer: an institution on the daily balance method that requires a 500 dollar minimum daily balance could also pay interest on the days that minimum is missed, provided the average daily balance for the month is at least 400 dollars.
Once the minimum is met, interest is owed on the whole balance. If 300 dollars is the minimum daily balance required to earn interest and a consumer deposits 500 dollars, the institution must pay the stated rate on the full 500 dollars, not on the 200 dollars above the threshold.
When Interest Accrues and When It Is Credited
Regulation DD ties the start of interest to the Expedited Funds Availability Act: interest must begin to accrue not later than the business day specified for interest-bearing accounts in section 606 of that Act and in section 229.14 of Regulation CC. At the other end, interest must accrue until the day funds are withdrawn. The interpretations illustrate the point: if a check is debited to an account on a Tuesday, the institution must accrue interest on those funds through Monday.
The regulation does not require any particular compounding or crediting frequency; an institution may compound annually, semiannually, quarterly, monthly, daily, continuously or on any other basis. Crediting dates, however, cannot be used to escape paying interest. If a consumer withdraws funds before a scheduled crediting date without closing the account, the institution may delay paying the accrued interest on the withdrawn amount until the crediting date, but may not avoid paying it.
Closing the account is treated differently. Subject to state or other law, an institution may choose not to pay accrued interest if the consumer closes an account before accrued interest is credited, but only if it has disclosed that fact; the account disclosures must state that interest will not be paid in that case.
Account Opening Disclosures
The APY reaches a consumer first through the account disclosures. A depository institution must provide them before an account is opened or a service is provided, whichever is earlier, and a service is treated as provided when a fee required to be disclosed is assessed. If the consumer is not present at the institution and has not already received the disclosures, the institution may mail or deliver them no later than 10 business days after the account is opened. That grace does not extend to accounts opened electronically: a consumer who is not present and uses an Internet site to open an account must receive the disclosures before the account is opened.
The disclosures must give the APY and the interest rate using those terms, and for variable-rate accounts how the rate is determined and how often it may change, together with the compounding and crediting frequency, minimum balances, the balance computation method, fees and bonuses.
Time accounts carry further items: the maturity date, the early withdrawal penalty and how it is calculated, and the renewal policy. Where interest compounds during the term and may be withdrawn before maturity, the disclosures must state that the APY assumes interest remains on deposit until maturity and that a withdrawal will reduce earnings.
Disclosures on Request and Oral Rate Inquiries
Institutions must also provide account disclosures to a consumer on request. When responding to a request, an institution may specify an interest rate and APY that were offered within the most recent seven calendar days, state that they are accurate as of an identified date, and give a telephone number for current rate information. It may also state the maturity of a time account as a term rather than a date.
Regulation DD separately governs the spoken word. In an oral response to a consumer's inquiry about interest rates payable on its accounts, the institution must state the APY; it may state the interest rate in addition, and no other rate may be stated. The interpretations add three limits. Institutions are not required to provide rate information orally at all. The advertising rules do not cover an oral response to a question about rates. And the rule does not apply to oral responses about existing accounts: a consumer holding a one-year certificate who asks about its rate during the term need not be told the APY.
Change-in-Terms Notices and Fixed-Rate Accounts
After an account is opened, a change in any term that must be disclosed requires advance notice to affected consumers if the change may reduce the APY or adversely affect the consumer. The notice must include the effective date and be mailed or delivered at least 30 calendar days before it. No notice is required for changes in the interest rate and corresponding APY in variable-rate accounts, for changes in check printing fees, or for changes in any term of a time account with a maturity of one month or less.
The definitions of fixed-rate and variable-rate accounts turn on that notice. A fixed-rate account is one for which the institution contracts to give at least 30 calendar days' advance written notice of decreases in the interest rate. A variable-rate account is one in which the rate may change after opening unless the institution has made that contractual promise. An account whose rate the bank can lower, but only after the promised written notice, is therefore a fixed-rate account for Regulation DD purposes, and its account disclosures must state the period the rate will be in effect.
Maturity Notices for Time Accounts
Time accounts with a maturity longer than one month that renew automatically require a notice before maturity. It must be mailed or delivered at least 30 calendar days before the existing account matures or, alternatively, at least 20 calendar days before the end of the grace period, provided the grace period is at least five calendar days.
For maturities longer than one year, the notice gives full account disclosures for the new account and the existing account's maturity date; for maturities of one year or less it may instead give the old and new maturity dates, the new rate and APY if known, and any change in terms.
Time accounts longer than one year that do not renew automatically require a shorter notice: at least 10 calendar days before maturity, the institution must disclose the maturity date and whether interest will be paid after maturity. Time accounts with a maturity of one month or less fall outside the maturity-notice rule altogether.
Advertising the Annual Percentage Yield
An advertisement that states a rate of return must state it as an "annual percentage yield" using that term. The abbreviation APY may be used provided the full term is stated at least once in the advertisement. No other rate may be stated, except that the interest rate, using that term, may appear in conjunction with, but not more conspicuously than, the APY to which it relates.
Stating an APY triggers further disclosures, to the extent applicable: for a variable-rate account, that the rate may change after the account is opened; the period the APY will be offered or that it is accurate as of a specified date; the minimum balance required to obtain it; the minimum deposit required to open the account, but only if that is greater than the minimum balance needed to obtain the advertised APY; a statement that fees could reduce the earnings; and, for time accounts, the term and a statement that a penalty will or may be imposed for early withdrawal.
Not every mention of rates is a trigger. The interpretations give examples that are not trigger terms: "One, three, and five year CDs available", "Bonus rates available", and "1% over our current rates" so long as the rates are not determinable from the advertisement.
Media Exemptions and Indoor Signs
Some media cannot carry a full set of disclosures, and the regulation relieves them of part of the list. An advertisement made through broadcast or electronic media such as television or radio, through outdoor media such as billboards, or through telephone response machines need not state the variable-rate notice, the period the APY is offered, the minimum opening deposit, the effect of fees, or the early withdrawal penalty statement, among other items. It must still state the APY and, for a time account, its term and the minimum balance needed to obtain the APY. The interpretations confine the exemption: it does not extend to advertisements posted on the Internet or sent by email.
Signs inside the premises of a depository institution or deposit broker are exempt from most of the advertising rules, but an indoor sign that states a rate of return must state it as an APY, using that term or "APY", may state the interest rate only in conjunction with it, and must advise consumers to contact an employee for further information about applicable fees and terms. Anything inside the premises that a consumer can keep, such as a brochure or a computer printout, is not an indoor sign and receives no exemption.
"Free", "No Cost" and Other Misleading Terms
Every advertisement, whatever its medium, must not be misleading or inaccurate or misrepresent the deposit contract. Two specific prohibitions follow. An account may not be described as "free" or "no cost", or by a similar term, if any maintenance or activity fee may be imposed on it. And the word "profit" may not be used in referring to interest paid on an account.
The interpretations define maintenance and activity fees broadly: fees imposed when a minimum balance is not met or a transaction limit is exceeded, transaction and service fees consumers reasonably expect to be imposed regularly, flat fees such as a monthly service fee, and fees to deposit, withdraw or transfer funds, including per-check or per-transaction charges such as 25 cents for each withdrawal. Check printing fees, balance inquiry fees, stop-payment fees, fees on checks returned unpaid and fees assessed against a dormant account are not maintenance or activity fees.
The term "fees waived" may not be used if a maintenance or activity fee may be imposed, because it is similar to "free". An account that is free only for a limited period, such as the first year after opening, may be advertised as free if the time period is also stated, and an account may be advertised as free for consumers meeting a condition unrelated to deposit accounts, such as being over 65.
Bonuses
A bonus under Regulation DD is a premium, gift, award or other consideration worth more than 10 dollars given or offered to a consumer during a year in exchange for opening, maintaining, renewing or increasing an account balance. Interest is not a bonus, and neither are items worth 10 dollars or less in a year, the waiver or reduction of a fee, or the absorption of expenses; a waived safe deposit box rental fee is not a bonus even if the fee exceeds 10 dollars.
To apply the 10 dollar threshold, institutions aggregate per account per calendar year the items that may be given under a specific promotion. The interpretations' example is an item worth 7 dollars offered for each calendar quarter in which a NOW account's average balance exceeds 10,000 dollars: because a consumer could receive items worth 28 dollars in the year, the bonus rules are triggered.
An advertisement that states a bonus must also state the APY and the time and balance requirements for the bonus; general statements such as "bonus checking" do not trigger those disclosures.
The APY Compared with the Loan APR
Borrowing uses a different measure under a different regulation. Regulation Z, at 12 CFR 1026.22, describes the annual percentage rate as a measure of the cost of credit, expressed as a yearly rate, that relates the amount and timing of value received by the consumer to the amount and timing of payments made. It is determined by the actuarial method or the United States Rule method, and it is driven by the finance charge, which section 1026.4 defines as the cost of consumer credit as a dollar amount, including interest, service charges, points, loan fees and similar charges imposed as an incident to the credit.
The two measures also carry different tolerances. A loan APR is generally considered accurate if it is within one-eighth of one percentage point of the correctly determined rate; in an irregular transaction, one with multiple advances, irregular payment periods or irregular payment amounts, the tolerance widens to one-quarter of one percentage point. The deposit APY's tolerance, by contrast, is the narrower one-twentieth of a percentage point described above.
Common Errors and Exam Traps
A common error is treating the APY as the rate plus some allowance for fees or bonuses. It reflects only interest and compounding over a 365-day period; bonuses and contingent earnings are excluded, and fees are not deducted, which is why advertisements must warn that fees could reduce earnings.
A second error is assuming the APY of a short certificate is the term's return doubled or quadrupled. The formula compounds the term's return over the year, so a six-month certificate's APY exceeds twice its six-month return.
A third error is reading the accuracy tolerance as a licence. The 0.05 point margin covers inadvertent errors and may not be built into the calculation on purpose.
A fourth error is assuming every bank product carries an APY; many products sold through a bank are not Regulation DD accounts.
Examination Relevance and Key Takeaways
Wherever an examination deals with deposit products and the comparison of savings vehicles, candidates should be able to compute an APY from interest, principal and term, explain why it differs from the interest rate and from a loan APR, and describe the Truth in Savings rules on paying interest, disclosing yields and advertising them, including the media exemptions and the restrictions on calling an account free.


