# "Simple interest rate of 0.10%" corresponds to "APY of 2.54%-5.00%"... how?

Balances above \$5,000 earn a simple interest rate of 0.10%, with a corresponding APY of 2.54%-5.00% APY.

I don't understand how a simple interest rate that is a fixed number can result in a range of APYs, especially one that varies over the range by almost a factor of 2.

What is the meaning of this statement, and how does the math work out?

• Given the two current answers, my bet is that the copy, as written is incomprehensible. And someone in marketing should be set straight. May 22, 2016 at 21:15
• @JoeTaxpayer: Yeah, I'm coming to the same conclusion... May 23, 2016 at 2:18

Aganju's response above is spot-on. The rationale for the range of APY is 'banking compliance regulations.' Our regulators require for the disclosure of what APY you could earn. Our Ultimate Account has tiered interest rates so if your balance was \$5,000 all month, you could earn 5.00%. But if your balance was \$10,000 then the corresponding APY would be 2.54%. Obviously there are countless iterations you could insert here for every balance possibility but the disclosure copy you see on our website is what our compliance folks felt best addressed the required deposit product advertising regulations.

I realize the explanation above may not have cleared up how the numbers are what they are but it should explain why you see a range of APY figures quoted.

Sincerely,

Bill Clancy, Northpointe Bank

• Thanks for your response, and welcome to Money.SE. Question for you: The \$10,000 deposit amount for the advertised low-end APY is completely arbitrary, right? Why did your compliance folks select that amount, and why did you opt not to include a mention of this \$10,000 amount in the advertising fine-print or on the rate disclosure page? May 23, 2016 at 15:37
• Yes, the \$10k is somewhat arbitrary. It seemed like using 2x the balance cap made sense intuitively in trying to show the APY for a balance above \$5,000. But we could have just as easily used \$7,500 or \$20,000. Good suggestion on including that info in the offer fine print - I'll get that suggestion over to the right folks on our team. Thanks! May 23, 2016 at 16:18
• @BillClancy: Thanks for the response! But please, don't put it in the fine print. Don't do anything with the \$10,000 at all, because it doesn't make any sense. There is actually nothing intuitively sensible about picking twice the minimum balance. Just say that the amount of the balance over \$5,000 receives a simple interest of 0.1% and then actually mention whether that is monthly or yearly or something else. Otherwise all you're going to do is mislead the user. May 23, 2016 at 17:46
• And it's worth mentioning that if your "regulators require disclosure for what APY you could earn", then you need to be telling the user that he could earn an APY as low as 0.1% and as high as 5.0%. Saying that the APY is between 2.54% and 5.0% is unfortunately nothing more than lying to the user when the reality is that it can be lower. May 23, 2016 at 19:59
• Thanks for the feedback. I understand the potential for confusion. The intent is to increase clarity but the actual outcome may be the reverse. In talking more with my compliance folks, the current version is what they feel best depicts the terms of the account and meets the spirit of the regulation. It seems you and I both feel it could be re-worded for clarity but a final decision has been made. :) May 23, 2016 at 21:18

It appears that qualifying accounts up to \$5,000 earn 5% APY. Anything above \$5,000 earns 0.1% (apparently per annum), so a total balance of \$10,000 earns 5% APY on one half and 0.1% on the other half. After one year that is

``````(5000 * 0.05) + (5000 * 0.001) = 255
``````

so 2.55% APY on \$10,000.

However, with higher balances the APY goes below 2.54%. In order to achieve a minimum APY of 2.54% the balance above \$5,000 needs to yield 2.5397% APY. It's not clear how that can relate to "simple interest" at 0.1%. ``````x = Balance
APY = 100 (Min[5000, x] * 0.05 + Max[0, (x - 5000)] * 0.025397) / x
``````

Perhaps there is a maximum balance allowed which limits the APY.

• Can I ask where you got \$10,000? What if I had \$100,000? How would the APY fall in the range given? May 22, 2016 at 7:52
• no. it's per year, pretty sure, when you think about it. Close enough to zero to average down. +1 for graph. May 22, 2016 at 12:19
• Edited my answer accordingly. May 24, 2016 at 7:51
• @ChrisDegnen The graph is wrong. The APY should converge on 0.1%. May 24, 2016 at 12:14
• @BenMiller The graph is showing that the rate for balance above \$5,000 needs to yield approx. 2.5397% APY for the minimum APY to be 2.54. The algorithm is shown below the graph. May 24, 2016 at 12:33

If you would've copied to sentence before this sentence, it would be quite obvious:

UltimateAccount annual percentage yield (APY) is 5.00% on balances up to \$5,000. Balances above \$5,000 earn a simple interest rate of 0.1 %.

So if your total is below 5000, you get 5%. Above 5000 you get 0.1%. Depending on your total, the average is between 5% and 0.1%; the more you have, the lower.

If you put 10000 in the account, the first 5000 give 5%, and the remaining 5000 give 0.1%, which adds to `5000*5%+5000*.1% = 250+5 = 255` = 2.55% of 10000 (The small difference to 2.54 is either rounding error, or comes from them only giving interest for 360 days instead of 365 per year (which is usual), and the APR is defined by law to reflect the annual effective rate.

If you put any number between 5000 and 10000 in the account, the summary APR lies between 5% and 2.55%. For example 6000 gives: `5000*5%+1000*.1% = 250 + 1 = 251`; 251 of 6000 is 4.183%. If you use 7000, you get `5000*5%+2000*.1% = 250 + 2 = 252`; 252 of 7000 is 3.6%. You should be able to repeat this math for any other number.

Each number between 5000 and 10000 gives an overall APR between 5% and 2.55%; the larger the input, the lower the average APR.

Note that that implies that either they assume nobody would put more than 10000 in such an account; or they assume this limit for cosmetic reasons (otherwise it would read '0.1 - 5%' APR, much uglier...); or the fine print states that there is no interest after 10000 at all.

• If it's really "obvious", can you explain where the 2.54% comes from? May 22, 2016 at 18:09
• Right. Why is that the floor? 100k invested and I'd be far closer to the .1%. May 22, 2016 at 20:41
• Looking at your edit, it seems like a long-winded way of saying "I don't know, either". The entire point of the question was that I didn't get how 1 number results in a range whose upper and lower bounds differ by a factor of 2, and your last note is saying you don't either. (And to be honest, it's the same with the previous answer, except that one came first so this is also a duplicate...) May 22, 2016 at 20:45
• then you completely misunderstand the answer. I thought it obvious, but it seems it isn't. I'll extend the answer further. May 22, 2016 at 21:55