Demystifying APY Calculations: Stepped-Rate and Promotional Rate Accounts Explained
When it comes to deposit accounts, there are various options available, each with its own features and benefits. Among these options are stepped-rate accounts and tiered-rate accounts. Calculating the Annual Percentage Yield (APY) for fixed and most variable-rate accounts is straightforward, and there does not seem to be much confusion on this. Likewise, the calculation of APYs for periodic statements is straightforward. However, we do receive a lot of questions on how to calculate the APY for purposes of account disclosures and advertisements for stepped-rate, variable-rate accounts with a promotional rate, and tiered-rate accounts. In this article, we will explore stepped-rate accounts and how to calculate the composite or blended APY for stepped-rate accounts and variable-rate accounts with an introductory premium or discount rate under Appendix A to Reg. DD (12 CFR Part 1030) and 12 CFR Part 707 for credit unions. In my next article, we will discuss how to calculate the various APYs for tiered-rate accounts.
A word of caution here: I am a compliance advisor and not a math scientist. All calculations below are to illustrate the steps involved in calculating the APY, and the numbers should not be taken as 100% accurate. Also, it should be noted that this applies to account disclosures and advertising. The calculations for periodic disclosures are slightly different. Because the Regulation requires the APY to be rounded and expressed to two decimal places, all our calculations will round to two decimal places. Unless stated otherwise, we will also assume that all accounts compound monthly.
General Formulas
Your first step in calculating the APY is determining the amount of interest the account will earn in the year (or the term for accounts with a stated maturity, e.g., a CD). While rounding can affect the APY slightly depending on the account balance used, the Regulation does not require you to use any specific balance. Unless stated otherwise, we will assume an account balance of $1,000.
For accounts without a stated maturity or with a term of 365 days, you use the following formula: 100 (Interest/Principal). For example, if you have a savings account that pays 4.00%, the account will earn $40.74 in interest. Plugging that into our formula, you get 100 (40.74/1000) = 4.07%.
The formula is a little more complex for accounts with a stated maturity other than 365 days: 100 (Interest/Principal). For example, you have a savings account that pays 4.00%. The account would earn $40.74 in interest. Plugging that into our formula, you get 100 (40.74/1000) = 4.07%.
For accounts with a stated maturity other than 365 days, the formula is a little more complex: 100 [(1 + Interest/Principal) (365/Days in term) −1]. Let’s assume that you had a 6-month CD (where there are 182 days in the term) that pays 4.00% with the interest compounded every six months. You would earn $20 in interest. Plugging that into our formula, you get [(1 + 20/1000) (365/182) −1] = 4.05%.
Stepped-Rate Accounts
A stepped-rate account is an account that offers two or more interest rates that take effect in succeeding periods and are known when the account is opened. For example, if you offer an account with an interest rate of 4.5% for the first 90 days and then it reverts to your standard 0.5% interest rate, this would be a stepped-rate account. An account that has an introductory rate of 4.5% for the first 90 days but then will revert to your prevailing rate at the conclusion of the 90-day period is a variable-rate account and not a stepped-rate account because you do not know what the rate will be after the 90 days.
In a stepped-rate account, an institution must calculate a composite or blended APY, assuming each interest rate is in effect for the length of time provided for in the deposit contract. Using the example above, where you offered an account that pays 4.5% for the first three months and then 0.5% thereafter, the account would earn $11.29 in interest in the first three months and another $3.80 in the remainder of the year, for a total of $15.09 interest earned in the year. Using the formula above, we get 100 (15.09/1,000) = 1.51%.
Variable-Rate Accounts with a Promotional Rate
Generally, with a variable-rate account, you calculate the APY as you would for a fixed-rate account, assuming the initial rate applies for the entire year (or term). This applies to a variable-rate account with an initial rate that is set at your prevailing rate but is fixed for an introductory period. However, when the account is paying a promotional rate (either a premium or discounted rate) for a fixed period and then will revert to the prevailing rate at the time, you calculate the APY similarly to a stepped-rate account, even though you do not know what the post-promotional rate will be. You would use the promotional rate for the promotional period and the prevailing rate (i.e., the rate that would currently apply to the account but for the promotional rate) for the remainder of the year or term. For example, if you offer an account that pays a promotional rate of 4.5% for the first 90 days and then will revert to the prevailing rate, which is currently 0.5%, you calculate the APY the same as the example above.
In conclusion, calculating the APY for stepped-rate accounts and variable-rate accounts with promotional rates requires specific formulas and considerations. While the process may seem complex, understanding the steps involved can help ensure accurate calculations. In the following article, we will delve into calculating the APYs for tiered-rate accounts.