# How does compound interest work with multiple bank accounts and percentage limits?

I found that Polish banks often offer smaller interest rates for amounts above a given threshold. For example this one (Google Translate) would make one earn 2.70% per year of amount below 100 000 PLN and then 1.9% for any amount above 100k. In order to maximize one's gains, would it make sense to set up multiple bank accounts to avoid going above their thresholds? How to calculate how to maximize the profit here?

Two example bank accounts rankings as for Feb 2016 (in Polish):

http://www.najlepszekonto.pl/ranking-kont-oszczednosciowych

http://www.bankier.pl/lokaty/porownaj-konta-oszczednosciowe

• Sorry, but isn't this entirely straight-forward? Keep your amounts below 100,000 PLN in each account, assuming the same interest rate in each account? What am I missing? – ChrisInEdmonton Feb 19 '16 at 14:24
• @ChrisInEdmonton: the thing is that there are accounts that offer higher interest rates that diminish after a much lower threshold - for example "Konto Oszczędnościowe Orange Finanse" would give 3.5% for amounts below 10k PLN. Also, I wonder how compound interest interacts with this one. – d33tah Feb 19 '16 at 14:25
• `I wonder how compound interest interacts with this one` Why is this a problem at all to calculate ? – DumbCoder Feb 19 '16 at 14:46
• @DumbCoder: because that's going to increase the amount of money I am going to calculate the interest for in the next month. So basically the problem I'm trying to solve is: given a set of banks B1, B2, B3, ... and thresholds T1, T2, T3, ... along with their interest rates I1, I2, I3, ..., how to select a set of banks that would make me maximize my interest? – d33tah Feb 19 '16 at 15:05
• @d33tah Max out the bank that pays the highest interest first and then move on to the next highest interest rate. That will maximize the interest earned. – Chris Feb 19 '16 at 16:52

would it make sense to set up multiple bank accounts to avoid going above their thresholds?

Quite possiblly yes but you need to pay attention to the fine print. I don't know what the situation is in poland but in the UK accounts that pay high interest often have strings attached. For example the santander 123 current account pays very good interest but it has an account fee and some other requirements that are difficult to meet if you are not using it as your "main current account".

You need to read the terms carefully, if you go over the threshold does the lower rate only apply to money over the threshold? or does it apply to all the money in the account? Are there any other restrictions on how you use the account.

Also I don't know if poland has any provisions for limited tax-advantaged savings (like the ISA scheme we have in the UK). If it does then that can add further complications.

How to calculate how to maximize the profit here?

Well in theory you would get the best account you can and fill it to the threshold. Then the next best account and so-on. You would move any interest paid in an account that was already full to the threshold to the best non-full account (or if the account strongly peanalises going over perhaps move an ammount of money equivilent to the interest just before the interest is paid).

In practice that is a lot of work, so if the rates on the different accounts are similar you may want to leave some margin for interest or (in the case of an account that pays the lower rate on the overage while still paying the higher rate on money below the threshold) accepting that some of your money will earn slightly less than idea.

Another option some accounts may offer is just to pay the interest to another account, avoiding the need to move it yourself.

Finally you should check out your government's limits for compensation in the event of banks going bust. As a general rule you don't want to put more than that ammount in a single bank even if doing so would get you the best interest.