Interest rate calculations

[mtbc]

I was thinking how tricky interest rate calculations might be for institutions. One typically wants to quote an annual percentage but give interest more often than that. In terms of how the payments add up to the annual total, we certainly don't want that sum to be less than the quoted percentage but we would also rather it be as low as possible. Yet, when we pay interest, it's not like we pay exactly a twelfth root or whatever, or probably even calculate roots as precisely as we could, and we somehow round each payment to probably just a couple of places depending on the currency we're using. Further, absent withdrawals, the interest payments increase steadily due to compounding. In practice, I wonder how institutions deal with such payment calculations where each is rounded yet what matters is the sum of the payments.

Comments

[armiphlage]

In Canada, it's mandatory that all interest rates be presented as an annual rate. So, "12% per annum, compounded monthly on the first of the month".

https://www.canada.ca/en/financial-consumer-agency/services/industry/commissioner-decisions/decision-55719-512Q304.html

[mtbc]

Mmm, that's exactly the kind of thing I wonder how they handle. E.g., if everything's rounded somehow to cents, and I have $1.00 and after a year expect to have $1.12, then is the bank going to give me 1¢ after the first month even though that reflects a rate of more than 12% if compound rather than simple interest? I suppose, maybe, but they'd also like to give me as little as possible overall.

[armiphlage]

It's stored as floating point; they round to two decimal places when displaying on a screen, or when transferring between accounts or businesses. When paying out as cash, it is rounded to the nearest 5 cents:

https://www.canada.ca/en/revenue-agency/programs/about-canada-revenue-agency-cra/phasing-penny.html

[mtbc]

If rounded fairly conventionally each month then if I have 50¢ and earn monthly interest then a 12% annual rate leaves me with still 50¢ at the end of the year. 60¢ would get me up to 72¢ at the end of the year, effectively a sweet 20%. Perhaps that's actually what happens, hmm.

Nice they're getting rid of the tiny change for cash though.