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It's easy to calculate interest on a fixed principal. If you have for example $1000 deposit on your savings account and the rate is 0.25% compounded every whatsoever and you want to know how much is the interest after some time then just use the formula for compound interest.

But what if you make irregular deposits and withdrawals? Say after a month, you deposit $500, then after another month you deposit $200, then after two months you withdraw $300, how do you calculate interest after a certain period of time?? What happens to the original principal?? Or is it like you compute compound interest for each deposit separately then get their sum? But what about the withdrawals???

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First, check the account’s terms and conditions regarding interest payments. Some don’t pay interest if you make a withdrawal that period. Others require a deposit in addition to no withdrawals.

Regardless of the ‘gotchas’, they should also tell you on what basis interest is earned. It could be the minimum balance that period. It could be the minimum balance each day, with interest calculated daily but only added to your account monthly, etc. Months might be calendar months, or they might be 30-day periods starting the day you opened your account, they might be missing a few days at the start or end if those days happened to be non-banking days (I’m not sure why - the missing days are included in another, possibly future, statement anyway, so why not put them where they belong?!).

There might also be strange adjustments to hold to a 360-day banking year.

Once you’ve worked all that out, use the formulas with your actual balances. It will almost certainly be more involved than a simple formula for compound interest.

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A typical approach is to compute interest daily on the balance of the account. You can make a spreadsheet that computes this. For each day, compute the interest from the previous day by multiplying the balance by 0.25%/365 (or 360 depending on the bank). Apply whatever rounding process the bank uses to get rid of fractional pennies. Then apply the day's transactions and you have the balance at the end of the day.

There is nothing special about the original principal. It is dollars in the account just like any subsequent deposit.

You can use the compound interest formula, just adding up the deposits and subtracting the withdrawals. If you deposited 500 45 days ago and withdrew 300 20 days ago, you now have 500(1+i)^44-300(1+i)^19 where i is the daily interest. It will give the same answer up to rounding.

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All the banks I have dealt with don't do the calculations as described in the answers by Lawrence and Ross Millikan but use a simplified method that works as follows. If the interest rate (APR) is, say, 0.24% per annum compounded monthly, then the amount of interest credited to the account at the end of the month is the average daily balance during the past month (taking into account all deposits and withdrawals made that month) times 0.02% with rounding to the nearest penny being done just that once instead of every day. The average daily balance is calculated by adding up all the daily balances over the past month and dividing by 30 (regardless of whether the month has 31 days or 30 days or 29 days or 28 days), which allows for special cases such as the account was opened in the middle of the month just concluded etc., and simplifies the banker's accounting practices.

It is important to understand that even if the interest is compounded daily, it is merely being accrued and doesn't appear in your account till the end of the month. As a general rule, you cannot access the accrued interest in the sense of withdrawing it from the account except if you close the account in which case, what you will get is the current balance plus accrued interest. That is, if the current account balance is $X and the accrued interest as of today is $Y, you can withdraw $X leaving a current balance of $0 (and so earning no more interest for the rest of the month) but you cannot withdraw $X + 0.5Y, say, because you don't have that much money in your account as yet. You can demand to close out your account and get $X + Y today but that is a drastic measure which you may or may not wish to take.

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