How is daily interest calculated on savings accounts?

On some bank accounts, it states that interest is calculated on a daily basis.

I’m presuming that means that each day the interest earned for that day is calculated based on the account balance at that time.

If so, how is it calculated?

Do they multiply the balance by the interest rate (to find what the annual interest earned on that amount would be) and then divide it by 365 to find the interest earned that day?

Or is it more complicated like they find the 365th root of the multiplier for the annual interest rate and apply that on a daily basis?

For example, in the latter case if the interest rate was 20% (not realistic but I’m choosing it because the numbers work out nicely), the annual multiplier would be 1.2 and the daily multiplier (to find the interest earned that day) would be 1.0005 – the 365th root of 1.2.

Is it one of these or is daily interest calculated in a different way?

Thanks

Comments

  • AmityNeon
    AmityNeon Posts: 891
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    edited 4 November 2023 at 4:33PM
    Interest does not compound daily so it would not be the 365th root. It's as simple as dividing the gross annual rate by 365 (or 366 during calender leap years), so the sum of the daily rates is equal to the annual rate.

    Gross annual rates for monthly interest are lower to account for monthly compounding.

    Even if interest was paid daily (and thus compounded daily), this would be factored into the published gross annual rate, so you would still just divide by the number of days in the year anyway.
  • masonic
    masonic Posts: 22,809
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    edited 4 November 2023 at 4:45PM
    The vast majority of accounts accrue simple interest on the closing balance of the account at the end of each day (subject to their cut-off time). Interest is therefore compounded at the frequency it is paid (i.e. monthly or annually). As above, divide the gross rate by 365 and that is the daily rate. Different providers may treat leap years differently.
    Exponentiation is only used if you wish to convert between gross rate and AER (where interest isn't paid annually). See https://en.wikipedia.org/wiki/Effective_interest_rate
  • aroominyork
    aroominyork Posts: 2,758
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    Is interest calculated on the balance at midnight (or another time of day)? If you withdraw funds in the morning and repay them later in the day, do you still receive the day's interest as if you had not touched your account that day?
  • masonic
    masonic Posts: 22,809
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    edited 4 November 2023 at 8:19PM
    Is interest calculated on the balance at midnight (or another time of day)? If you withdraw funds in the morning and repay them later in the day, do you still receive the day's interest as if you had not touched your account that day?
    It's not usually midnight, often late afternoon or early evening. If you search around you can probably find information about banks' cut-off times, but they don't like to publicise them. It can lead people to exploiting differences to earn double interest on the same cash (which can cause banks to end their relationship with you, as some have found).
    Generally money moved out early in the day and replaced by mid-afternoon would not lose a day's interest. But YMMV.
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