interest compounded daily vs monthly

Question

I want to compare two saving accounts with same APY, but one has interest "compounded daily and credited monthly" and the other has interest "compounded monthly and credited monthly". Which will yield greater interest after a year if I make a deposit of a certain amount to the account every week in that year?

Question 1 (directly related to my question above): If the interest is compounded monthly, what is the principal for a month if I deposit or withdraw a few times during that month? Is it the average daily balance of that month?

Question 2 (not directly related to my original question): Does the frequency of crediting interest affect APY, assuming the same APR and compounding frequency? I guess not. The interest is earned after each compounding, but it may not be credited to your account immediately, as it is often too small. However, the interest you earned on that day (assume daily compounding) will be included in the principal to generate the interest for the next day. Is my understanding correct? If so, then no matter when you get the interest, the interest is always helping you earn more interest.

Answer 1

If you deposited $100 into each, you'd have the same at the end of the year in both, because the APY is the same. APY already factors in compounding as you already know.

Which will yield greater interest after a year if I make a deposit of a certain amount to the account every week in that year?

It would depend on which balance the monthly compounding account uses.

Question 1: If the interest is compounded monthly, what is the principal for a month if I deposit or withdraw a few times during that month?

Compounding daily is standard for many accounts as balances can fluctuate over the month. You'd have to consult the account terms for the monthly-compounding account to find out which balance it uses, it could be average daily balance but I wouldn't assume that.

Question 2: Does the frequency of crediting interest affect APY, assuming the same APR and compounding frequency?

No, APR and compounding frequency determine APY independent of payment frequency.

Answer 2

APY is the abbreviation of annual percentage yield, it's already taking into account of compounding, and tells you directly how much you earn if you deposit for a year.

So if you deposit $10000 in 2% APY account, you will have $10200 after a year ($200 interest), whether it's compounding monthly, daily, or every nanosecond.

APR is the abbreviation of annual percentage rate, and can only be used to compute the return accurately if you know the compounding period. For example, if you deposit $10000 in 2% APR account, compounding every half year, then you will have 10000*(1+2%/2)^2 dollars. If it's compounding every month, you will have 10000*(1+2%/12)^12 dollars. If you have n compounding period in a year, then you will have 10000*(1+2%/n)^n dollars. If you let n goes to infinity (continuously compounding), you will have 10000*exp(0.02) dollars, etc.