# How do banks calculate interst on savings account

Sometimes, I see banks advertise rates on savings accounts like this: Interest is calculated daily and compounded semi annually. Now if it is compounded semi annually , how can it be calculated daily? If, interest is 4%, compounded semi annually, then 100\$ at the end of the year will become 102^2 = 104.04.

So where does the daily calculation come into play?

So the interest is quoted as 4% calculated daily, and compounded semi-annually.

If you simply dropped \$100 into this account on Jan 1 and did nothing else, then the only activity you would see would be a deposit of \$2.00 on June 30, and a further deposit of \$2.04 on Dec 31. The only time that the "calculated daily" takes effect is when there are cash flows into or out of the account during the year.

A rate of 4% a year is the equivalent of 4/365 or 0.010959% per day.

So as cash flowed into and out of the account, each day someone would calculate how much interest the balance in the account for that day had earned for that day. The amount of this interest would be recorded somewhere, but would not appear anywhere in the account balance.

Since the interest is compounded semi-annually, on June 30 and Dec 31 the accumulated total of this interest would be credited to the account and would then begin to accumulate interest-on-interest, i.e. "compound"

I can recall, in the dim distant days of my youth, where interest was calculated (possibly on an abacus) compounded semi-annually based on the minimum semi-annual balance!

• Thanks...that was the missing link....it has to do with cash flowing in and out of the account . – Victor123 Feb 7 '15 at 15:47
• Now, the interesting thing happens when the interest is "calculated daily, compounded semi-annually, and paid monthly". What happens in that scenario? – Joe Z. Mar 28 '15 at 16:50

The way I understand it, the daily calculation means that you accrue interest every day, enough so that if you keep the same balance in your account, it would effectively be 2% every 183 days. This would be 1.02 to the power of 1/183, which is about 0.010821% daily interest.

The accrued interest would then get applied to your account about once every month, as described in this question.