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Why are there two APY function keys on the PROM Truth-in-Savings Compliance tool?

The [APY/%] key is used to compute the A.P.Y. for non-time (no maturity date) accounts such as savings accounts, N.O.W. accounts, etc. The term is assumed to be 1 year, and no principal amount is entered. You can calculate the A.P.Y. from an interest rate using any compounding interval, and you can calculate the interest rate from the A.P.Y. The [APY/Int] key is used to compute the A.P.Y. for time accounts (with a specified maturity date), such as certificates of deposit. You can use the [APY/Int] routine to compute the A.P.Y. for advertising, lobby signs, and account disclosures (see next question), and to compute the A.P.Y. earned for periodic statements.

How do I compute the A.P.Y. for advertisements, lobby signs, and account disclosures?

There are basically two types of accounts: time accounts with a specified maturity date, and accounts with no maturity date. For those without a maturity date, use the [APY/%] function key which assumes a maturity date of one year. With this routine, you can quickly convert from an interest rate to the A.P.Y. and from the A.P.Y. to an interest rate. For time accounts with a known maturity date, use the [APY/Int] function key. When the "PRIN" prompt appears, enter 10,000. The interest earned and A.P.Y. will be calculated for the term of the deposit. In the advertisement and account disclosure, you don't actually show the principal amount or interest earned, just the interest rate and A.P.Y. However, it is necessary to compute an interest amount in order to calculate the A.P.Y. percentage.

How do I compute the A.P.Y. when the depositor withdraws the interest (rather than leaving it on deposit)?

The major consideration here is whether the depositor is required  to withdraw the interest. If withdrawal is not mandatory, the A.P.Y. is disclosed as if the interest is left on deposit. If interest withdrawals are required, the A.P.Y. must show the effect of the interest withdrawals. In this case, the total interest paid over the term of the deposit will be less than if the interest were left on deposit. The [APY/Int] function key is used to make this calculation.

If interest is not compounded, use the [APY/Int] function key and enter a compounding frequency of 0 to compute the interest amount and A.P.Y. Note that, although it is unlikely, it is possible to have an account in which the interest is compounded and withdrawals are required. For example, an account could have daily compounding of interest and require withdrawal of the interest each month. The difficulty here is computing the actual amount of interest that would be paid over the period of the time account. Once you have that amount, you can use the [APY/Int] function key to compute the A.P.Y. (For our example, you could compute the amount of interest paid in each month during the term to get the total interest paid, and then compute the A.P.Y. using the [APY/Int] function key.)

What is the difference between Tiering Method "A" and Method "B"?

Tiering method "A" assumes interest is paid on the entire deposit amount at the interest rate in the particular band that the deposit amount falls. For advertising and account disclosures, the A.P.Y. must be disclosed for each band. For non-time accounts, the [APY/%] routine is used for each band. For time accounts, the [APY/Int] routine is well as for calculating the A.P.Y. earned (in the case of periodic statements).

Tiering method "B" assumes an interest rate is paid only on that portion of the deposit within the specified tier. The [Tier] function key is used to calculate a minimum and maximum A.P.Y. for each tier level.

How do I calculate interest with no compounding?

If interest is computed without any compounding, i.e., at the maturity date of the account, use the [APY/Int] function key and enter a compounding frequency of 0. For example, a one-year \$1000 deposit at 5% interest would earn exactly \$50 in interest.

If the term of the deposit is exactly one year, the A.P.Y. will be the same as the interest rate. If the term is less than one year, the A.P.Y. will be slightly higher, and if the term is more than one year, the A.P.Y. will be slightly lower. (See the next question for an explanation of this.)

For time accounts over one year with no compounding, why is the A.P.Y. less than the interest rate?

The basic formulas in Regulation DD use annual compounding. The intent is to provide a uniform measurement system to report the interest earned, as a percentage, to depositors. As shown in the above question, a one-year deposit with no compounding will result in an interest rate equal to the A.P.Y. (In this case, the interest is actually compounded once, at the end of the year.) If the term of the transaction is longer than one year, the interest is compounded only once, at the end of the term. For a two-year period, the compounding interval is two years. It is common knowledge that if you compound interest more often, the amount of interest paid increases. The reverse is true if you compound interest less often--the amount of interest decreases. In our example, compounding the interest once every two years will result in a lower amount of interest paid than if we compounded it annually.

Because Regulation DD computes the A.P.Y. based on annual compounding, the A.P.Y. for a two-year deposit will be less than the interest rate. In order to keep the A.P.Y. the same as the interest rate, you need to compound the interest annually. This can be done by entering a compounding frequency of 1 in the Truth-in-Savings Compliance Tool.

What is the difference between no compounding and compounding at the end of the term?

There is no difference. The phrase "no compounding" is often used to describe the practice of computing the interest at the end of the term. For example, if we compute the interest earned on a 30-day, \$5000 certificate of deposit at 5% as

5000 x .05 / 365 x 30

we get \$20.55 of interest and an A.P.Y. of 5.1169%. The interest is not compounded during the term of the deposit, thus the phrase "no compounding". If we used daily compounding for this same deposit, the interest amount would be \$20.59 and the A.P.Y. 5.1271%

How many decimal places should the A.P.Y. percentage be disclosed to?

Regulation DD clearly states that the A.P.Y. should be disclosed to two decimal places in all cases except for account disclosures, where more decimal places can be shown if desired. Refer to Section 230.3: General Disclosure Requirements, paragraph (f). The "Fed" has made it clear that it does not want more than two decimal places used except for account disclosures. The Truth-in-Savings Compliance Tool will make calculations to two or four places -- see the Setup Routine Section in the User's Guide to change the precision.

What is the difference between the A.P.Y. and the A.P.Y. Earned?

The A.P.Y. Earned is required for periodic statement disclosures (See Section 230.6). The calculation methods for the A.P.Y. earned were amended by the Fed on March 19, 1993 for certain types of accounts with periodic statements. The A.P.Y. is used for advertising, account disclosures and other accounts.

What is the difference between compounding interval and compounding frequency?

"Compounding interval" is defined in the March 19th, 1993 amendment to Regulation DD to be "the number of days in each compounding period." Thus, for daily compounding, the compounding interval is 1 day. The term "compounding frequency", although not used in the regulation, is commonly used in the banking industry to indicate the number of times interest is compounded during a year. Thus a compounding interval of 1 day is equivalent to a compounding frequency of 365. (One can use either 365 or 366 in a leap year, however, the difference in A.P.Y. calculations is virtually negligible).

The Truth-in-Savings Compliance Tool uses the term compounding frequency in its routines because the term is more commonly understood.