# Demystifying APY Calculations: Tiered Rate Accounts Explained

Blog,
Jon Tavares – Senior Compliance Consultant

In a previous article Demystifying APY Calculations:  Stepped Rates and Promotional Rates Explained, we discussed how to calculate the Annual Percentage Yield (APY) for stepped-rate and promotional-rate accounts. Now, we will delve into the two types of tiered-rate accounts and explore the methodology to calculate each APY. When an account offers multiple interest rates based on specified balance levels, financial institutions are required to calculate the APY using a specific method. Additionally, accounts that use tiering method B must disclose the APY or a range of APYs for each balance tier.

Let’s take a closer look at the two tiering methods and the corresponding calculations for each tier. In the following examples, let’s assume that a financial institution pays:

• 4.65% interest on balances up to \$2,500;
• 4.85% interest on balances more than \$2,500 up to but not exceeding \$5,000; and
• 5.00% interest on balances more than \$5,000.
###### Tiering Method A

Under this method, the institution pays the stated interest rate on the entire balance in the account that corresponds to the applicable deposit tier. For example, if my girlfriend Ana de Armas and I deposit \$5,000, the institution pays the 4.85% interest rate on the entire \$8,000.

When this method is used, only one APY applies to each tier, and the APY remains constant within each tier regardless of the principal amount assumed to have been deposited.

In advertisements and account opening disclosures, the institution will state three APYs – one for each balance tier. The calculation of each APY is like that of accounts with a single interest rate. The calculation considers the total interest earned by the consumer within each tier for a year and the principal assumed to have been deposited to earn that amount of interest. Because this calculation is straightforward and is calculated the same as a normal account, we won’t discuss the APY calculation here. If you need a more detailed explanation, please refer to Appendix A of Regulation DD (12 CFR Part 1030, App. A).

###### Tiering Method B

Under this method, the institution pays the stated interest rate only on the portion of the balance within the specified tier. For example, if Ana and I deposit \$8,000, the institution pays 4.65% on \$2,500, 4.85% on the next \$2,500 (the difference between \$5,000, the second-tier cut-off, and the first-tier cut-off of \$2,500), and 5.00% on \$3,000 (the difference between \$8,000 and the second-tier cut-off).

When using this method, the institution must provide a range that shows the lowest and highest APYs for each tier, except for the first tier, which would be calculated the same as Method A. The low end of the APY 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 (i.e., for tier two above, an institution would use \$2,500.01). The high end is based on the interest paid by the institution on the highest principal that could be deposited to earn the same interest rate (i.e., for tier two above, an institution would use \$5,000.00). If the account does not have a maximum deposit limit, the institution may assume any reasonable amount (e.g., for tier three above, an institution may use \$10,000.00, \$100,000.00, \$1,000,000.00, or any other reasonable amount. For the calculations below, we will use \$250,000.00 for the high end of tier three).

First tier:

Assuming daily compounding, if a \$2,500 deposit earns \$118.99 in interest, the APY for the first tier is calculated using the simple formula:

APY = 100 * (118.99/2,500)

APY = 4.76%

Second tier:

For the second tier, the institution would pay between \$118.99 and \$243.22 in interest based on assumed balances of \$2,500.01 and \$5,000, respectively. For \$2,500.01, interest is calculated on \$2,500 at a 4.65% interest rate, plus interest on \$0.01 at a 4.85% rate. For the low end of the second tier, the APY is 4.76% using the simple formula:

APY = 100 * (118.99/2,500.01)

APY = 4.76%

For \$5,000, interest is calculated on \$2,500 at a 4.65% interest rate, plus interest on \$2,500 at a 4.85% interest rate. For the high end of the second tier, the APY is 4.86%:

APY = 100 * (243.22/5,000)

APY = 4.86%

Thus, the APY range for the second tier is 4.76% to 4.86%

Third tier:

For the third tier, if the low end of the tier (\$5,000.01) earns \$243.22 in interest, the APY is calculated using the simple formula:

APY = 100 * (243.22/5,000.01)

APY = 4.86%

Since there is no limit, we will assume a balance of \$250,000 for the high-end. For this amount, interest is calculated on \$2,500 at a 4.65% interest rate, plus interest on \$2,500 at a 4.85% rate, plus interest on \$245,000 at a 5.00% rate. For the high end of the third tier, the APY is 5.12%:

APY = 100 * (12,803.76/250,000)

APY = 5.12%

The third-tier APY range would be stated as 4.86% to 5.12%.

Understanding the different methods of tiered interest rates and how to calculate the Annual Percentage Yield for each can help ensure proper disclosure of the APY in advertisements and account opening disclosures.

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Blog,
Jon Tavares – Senior Compliance Consultant