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6500  Consumer Financial Protection Bureau
Appendix A to Part 1030—Annual Percentage Yield Calculation
The annual percentage yield measures the total amount of interest
paid on an account based on the interest rate and the frequency of
compounding. The annual percentage yield reflects only interest and
does not include the value of any bonus (or other
consideration
worth $10 or less) that may
be provided to the consumer to open, maintain, increase or renew an
account. Interest or other earnings are not to be included in the
annual percentage yield if such amounts are determined by circumstances
that may or may not occur in the future. The annual percentage yield is
expressed as an annualized rate, based on a 365day year. Institutions
may calculate the annual percentage yield based on a 365day or a
366day year in a leap year. Part I of this appendix discusses the
annual percentage yield calculations for account disclosures and
advertisements, while Part II discusses annual percentage yield earned
calculations for periodic statements.
Part I. Annual Percentage Yield for Account Disclosures and
Advertising Purposes
In general, the annual percentage yield for account disclosures
under §§ 1030.4 and 1030.5 and for advertising under § 1030.8 is
an annualized rate that reflects the relationship between the amount of
interest that would be earned by the consumer for the term of the
account and the amount of principal used to calculate that interest.
Special rules apply to accounts with tiered and stepped interest rates,
and to certain time accounts with a stated maturity greater than one
year.
A. General Rules
Except as provided in Part I.E. of this appendix, the annual
percentage yield shall be calculated by the formula shown below.
Institutions shall calculate the annual percentage yield based on the
actual number of days in the term of the account. For accounts without
a stated maturity date (such as a typical savings or transaction
account), the calculation shall be based on an assumed term of 365
days. In determining the total interest figure to be used in the
formula, institutions shall assume that all principal and interest
remain on deposit for the entire term and that no other transactions
(deposits or withdrawals) occur during the term. This assumption shall
not be used if an institution requires, as a condition of the account,
that consumers withdraw interest during the term. In such a case, the
interest (and annual percentage yield calculation) shall reflect that
requirement. For time accounts that are offered in multiples of months,
institutions may base the number of days on either the actual number of
days during the applicable period, or the number of days that would
occur for any actual sequence of that many calendar months. If
institutions choose to use the latter rule, they must use the same
number of days to calculate the dollar amount of interest earned on the
account that is used in the annual percentage yield formula (where
"Interest" is divided by "Principal").
The annual percentage yield is calculated by use of the following
general formula ("APY" is used for convenience in the formulas):
APY = 100 [(1 + Interest/Principal)(365/Days in term)1]
"Principal" is the amount of funds assumed to have been
deposited at the beginning of the account.
"Interest" is the total dollar amount of interest earned on
the Principal for the term of the account.
"Days in term" is the actual number of days in the term of the
account. When the "days in term" is 365 (that is, where the
stated maturity is 365 days or where the account does not have a stated
maturity), the annual percentage yield can be calculated by use of the
following simple formula:
APY=100 (Interest/Principal)
Examples
(1) If an institution pays $61.68 in interest for a 365day year
on $1,000 deposited into a NOW account, using the general formula
above, the annual percentage yield is 6.17%:
APY = 100 [(1 + 61.68/1,000) (365/365)  1]
APY = 6.17%
Or, using the simple formula above (since, as an account without a
stated term, the term is deemed to be 365 days):
APY = 100 (61.68/1,000)
APY = 6.17%
(2) If an institution pays $30.37 in interest on a $1,000
sixmonth certificate of deposit (where the sixmonth period used by
the institution contains 182 days), using the general formula above,
the annual percentage yield is 6.18%:
APY = 100 [(1 + 30.37/1,000) (365/182)  1]
APY = 6.18%
B. SteppedRate Accounts (Different Rates Apply in Succeeding
Periods)
For accounts with two or more interest rates applied in succeeding
periods (where the rates are known at the time the account is opened),
an institution shall assume each interest rate is in effect for the
length of time provided for in the deposit contract.
Examples
(1) If an institution offers a $1,000 6month certificate of
deposit on which it pays a 5% interest rate, compounded daily, for the
first three months (which contain 91 days), and a 5.5% interest rate,
compounded daily, for the next three months (which contain 92 days),
the total interest for six months is $26.68 and, using the general
formula above, the annual percentage yield is 5.39%:
APY = 100 [(1 + 26.68/1,000) (365/183)  1]
APY = 5.39%
(2) If an institution offers a $1,000 twoyear certificate of
deposit on which it pays a 6% interest rate, compounded daily, for the
first year, and a 6.5% interest rate, compounded daily, for the next
year, the total interest for two years is $133.13, and, using the
general formula above, the annual percentage yield is 6.45%:
APY = 100 [(1 + 133.13/1,000) (365/730)  1]
APY = 6.45%
C. VariableRate Accounts
For variablerate accounts without an introductory premium or
discounted rate, an institution must base the calculation only on the
initial interest rate in effect when the account is opened (or
advertised), and assume that this rate will not change during the year.
Variablerate accounts with an introductory premium (or discount)
rate must be calculated like a steppedrate account. Thus, an
institution shall assume that: (1) The introductory interest rate is in
effect for the length of time provided for in the deposit contract; and
(2) the variable interest rate that would have been in effect when the
account is opened or advertised (but for the introductory rate) is in
effect for the remainder of the year. If the variable rate is tied to
an index, the indexbased rate in effect at the time of disclosure must
be used for the remainder of the year. If the rate is not tied to an
index, the rate in effect for existing consumers holding the same
account (who are not receiving the introductory interest rate) must be
used for the remainder of the year.
For example, if an institution offers an account on which it pays a
7% interest rate, compounded daily, for the first three months (which,
for example, contain 91 days), while the variable interest rate that
would have been in effect when the account was opened was 5%, the
total interest for a 365day year for a $1,000 deposit is $56.52 (based
on 91 days at 7% followed by 274 days at 5%). Using the simple
formula, the annual percentage yield is 5.65%:
APY = 100 (56.52/1,000)
APY = 5.65%
D. TieredRate Accounts (Different Rates Apply to Specified
Balance Levels)
For accounts in which two or more interest rates paid on the account
are applicable to specified balance levels, the institution must
calculate the annual percentage yield in accordance with the method
described below that it uses to calculate interest. In all cases, an
annual percentage yield (or a range of annual percentage yields, if
appropriate) must be disclosed for each balance tier.
For purposes of the examples discussed below, assume the following:
Interest rate
(percent)

Deposit balance required to earn rate

5.25

Up to but not exceeding $2,500.

5.50

Above $2,500
but not exceeding $15,000.

5.75

Above $15,000.

Tiering Method A. Under this method, an
institution pays on the full balance in the account the stated interest
rate that corresponds to the applicable deposit tier. For example, if a
consumer deposits $8,000, the institution pays the 5.50% interest rate
on the entire $8,000.
When this method is used to determine interest, only one annual
percentage yield will apply to each tier. Within each tier, the annual
percentage yield will not vary with the amount of principal assumed to
have been deposited.
For the interest rates and deposit balances assumed above, the
institution will state three annual percentage yieldsone
corresponding to each balance tier. Calculation of each annual
percentage yield is similar for this type of account as for accounts
with a single interest rate. Thus, the calculation is based on the
total amount of interest that would be received by the consumer for
each tier of the account for a year and the principal assumed to have
been deposited to earn that amount of interest.
First tier. Assuming daily compounding, the institution
will pay $53.90 in interest on a $1,000 deposit. Using the general
formula, for the first tier, the annual percentage yield is 5.39%:
APY = 100 [(1 + 53.90/1,000) (365/365)  1]
APY = 5.39%
Using the simple formula:
APY = 100 (53.90/1,000)
APY = 5.39%
Second tier. The institution will pay $452.29 in interest
on an $8,000 deposit. Thus, using the simple formula, the annual
percentage yield for the second tier is 5.65%:
APY = 100 (452.29/8,000)
APY = 5.65%
Third tier. The institution will pay $1,183.61 in
interest on a $20,000 deposit. Thus, using the simple formula, the
annual percentage yield for the third tier is 5.92%:
APY = 100 (1,183.61/20,000)
APY = 5.92%
Tiering Method B. Under this method, an institution pays
the stated interest rate only on that portion of the balance within the
specified tier. For example, if a consumer deposits $8,000, the
institution pays 5.25% on $2,500 and 5.50% on $5,500 (the difference
between $8,000 and the first tier cutoff of $2,500).
The institution that computes interest in this manner must provide a
range that shows the lowest and the highest annual percentage yields
for each tier (other than for the first tier, which, like the tiers in
Method A, has the same annual percentage yield throughout). The low
figure for an annual percentage yield range is calculated based on the
total amount of interest earned for a year assuming the minimum
principal required to earn the interest rate for that tier. The high
figure for an annual percentage yield range is based on the amount of
interest the institution would pay on the highest principal that could
be deposited to earn that same interest rate. If the account does not
have a limit on the maximum amount that can be deposited, the
institution may assume any amount.
For the tiering structure assumed above, the institution would state
a total of five annual percentage yieldsone figure for the first tier
and two figures stated as a range for the other two tiers.
First tier. Assuming daily compounding, the institution
would pay $53.90 in interest on a $1,000 deposit. For this first tier,
using the simple formula, the annual percentage yield is 5.39%:
APY = 100 (53.90/1,000)
APY = 5.39%
Second tier. For the second tier, the institution would
pay between $134.75 and $841.45 in interest, based on assumed balances
of $2,500.01 and $15,000, respectively. For $2,500.01, interest would
be figured on $2,500 at 5.25% interest rate plus interest on $.01 at
5.50%. For the low end of the second tier, therefore, the annual
percentage yield is 5.39%, using the simple formula:
APY = 100 (134.75/2,500)
APY = 5.39%
For $15,000, interest is figured on $2,500 at 5.25% interest rate
plus interest on $12,500 at 5.50% interest rate. For the high end of
the second tier, the annual percentage yield, using the simple formula,
is 5.61%:
APY = 100 (841.45/15,000)
APY = 5.61%
Thus, the annual percentage yield range for the second tier is
5.39% to 5.61%.
Third tier. For the third tier, the institution would pay
$841.45 in interest on the low end of the third tier (a balance of
$15,000.01). For $15,000.01, interest would be figured on $2,500 at
5.25% interest rate, plus interest on $12,500 at 5.50% interest rate,
plus interest on $.01 at 5.75% interest rate. For the low end of the
third tier, therefore, the annual percentage yield (using the simple
formula) is 5.61%:
APY = 100 (841.45/15,000)
APY = 5.61%
Since the institution does not limit the account balance, it may
assume any maximum amount for the purposes of computing the annual
percentage yield for the high end of the third tier. For an assumed
maximum balance amount of $100,000, interest would be figured on $2,500
at 5.25% interest rate, plus interest on $12,500 at 5.50% interest
rate, plus interest on $85,000 at 5.75% interest rate. For the high
end of the third tier, therefore, the annual percentage yield, using
the simple formula, is 5.87%.
APY = 100 (5,871.79/100,000)
APY = 5.87%
Thus, the annual percentage yield range that would be stated for the
third tier is 5.61% to 5.87%.
If the assumed maximum balance amount is $1,000,000 instead of
$100,000, the institution would use $985,000 rather than $85,000 in the
last calculation. In that case, for the high end of the third tier the
annual percentage yield, using the simple formula, is 5.91%:
APY = 100 (59,134.22/1,000,000)
APY = 5.91%
Thus, the annual percentage yield range that would be stated for the
third tier is 5.61% to 5.91%.
E. Time Accounts With a Stated Maturity Greater Than One Year
That Pay Interest at Least Annually
1. For time accounts with a stated maturity greater than one year
that do not compound interest on an annual or more frequent basis, and
that require the consumer to withdraw interest at least annually, the
annual percentage yield may be disclosed as equal to the interest rate.
Example
(1) If an institution offers a $1,000 twoyear certificate of
deposit that does not compound and that pays out interest semiannually
by check or transfer at a 6.00% interest rate, the annual percentage
yield may be disclosed as 6.00%.
(2) For time accounts covered by this paragraph that are also
steppedrate accounts, the annual percentage yield may be disclosed as
equal to the composite interest rate.
Example
(1) If an institution offers a $1,000 threeyear certificate of
deposit that does not compound and that pays out interest annually by
check or transfer at a 5.00% interest rate for the first year, 6.00%
interest rate for the second year, and 7.00% interest rate for the
third year, the institution may compute the composite interest rate and
APY as follows:
(a) Multiply each interest rate by the number of days it will be
in effect;
(b) Add these figures together; and
(c) Divide by the total number of days in the term.
(2) Applied to the example, the products of the interest rates and
days the rates are in effect are (5.00% × 365 days) 1825, (6.00% ×
365 days) 2190, and (7.00% × 365 days) 2555, respectively. The sum of
these products, 6570, is divided by 1095, the total number of days in
the term. The composite interest rate and APY are both 6.00%.
Part II. Annual Percentage Yield Earned for Periodic
Statements
The annual percentage yield earned for periodic statements under
§ 1030.6(a) is an annualized rate that reflects the relationship
between the amount of interest actually earned on the consumer's
account during the statement period and the average daily balance in
the account for the statement period. Pursuant to § 1030.6(b),
however, if an institution uses the average daily balance method and
calculates interest for a period other than the statement period, the
annual percentage yield earned shall reflect the relationship between
the amount of interest earned and the average daily balance in the
account for that other period.
The annual percentage yield earned shall be calculated by using the
following formulas ("APY Earned" is used for convenience in the
formulas):
A. General Formula
APY Earned = 100 [(1 + Interest earned/Balance) (365/Days in
period)  1]
"Balance" is the average daily balance in the account for the
period.
"Interest earned" is the actual amount of interest earned on
the account for the period.
"Days in period" is the actual number of days for the period.
Examples
(1) Assume an institution calculates interest for the statement
period (and uses either the daily balance or the average daily balance
method), and the account has a balance of $1,500 for 15 days and a
balance of $500 for the remaining 15 days of a 30day statement period.
The average daily balance for the period is $1,000. The interest earned
(under either balance computation method) is $5.25 during the period.
The annual percentage yield earned (using the formula above) is 6.58%:
APY Earned = 100 [(1 + 5.25/1,000) (365/30)  1]
APY Earned = 6.58%
(2) Assume an institution calculates interest on the average daily
balance for the calendar month and provides periodic statements that
cover the period from the 16th of one month to the 15th of the next
month. The account has a balance of $2,000 September 1 through
September 15 and a balance of $1,000 for the remaining 15 days of
September. The average daily balance for the month of September is
$1,500, which results in $6.50 in interest earned for the month. The
annual percentage yield earned for the month of September would be
shown on the periodic statement covering September 16 through October
15. The annual percentage yield earned (using the formula above) is
5.40%:
APY Earned = 100 [(6.50/1,500) (365/30)  1]
APY Earned = 5.40%
(3) Assume an institution calculates interest on the average daily
balance for a quarter (for example, the calendar months of September
through November), and provides monthly periodic statements covering
calendar months. The account has a balance of $1,000 throughout the 30
days of September, a balance of $2,000 throughout the 31 days of
October, and a balance of $3,000 throughout the 30 days of November.
The average daily balance for the quarter is $2,000, which results in
$21 in interest earned for the quarter. The annual percentage yield
earned would be shown on the periodic statement for November. The
annual percentage yield earned (using the formula above) is
4.28%:
APY Earned = 100 [(1 + 21/2,000) (365/91)  1]
APY Earned = 4.28%
B. Special Formula for Use Where Periodic Statement Is Sent
More Often Than the Period for Which Interest Is Compounded
Institutions that use the daily balance method to accrue interest
and that issue periodic statements more often than the period for which
interest is compounded shall use the following special
formula:
The following definition applies for use in this formula (all other
terms are defined under Part II):
"Compounding" is the number of days in each compounding
period.
Assume an institution calculates interest for the statement period
using the daily balance method, pays a 5.00% interest rate, compounded
annually, and provides periodic statements for each monthly cycle. The
account has a daily balance of $1,000 for a 30day statement period.
The interest earned is $4.11 for the period, and the annual percentage
yield earned (using the special formula above) is
5.00%:
APY Earned = 5.00%
[Codified to 12 C.F.R. Part 1030, Appendix
A]
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