In financial terminology, "accrues" means the same thing as "accumulates." Interest is considered accrued when it is added to the balance on the account. Interest accrues on loans, such as a mortgage, or on savings accounts and investments. Daily accrual means interest amounts are added to the account balance every day.
Interest can accrue on any time schedule; common periods include daily, monthly and annually. Some modern computations have interest accrue continuously based on mathematical formulas that slice time more and more finely as time approaches zero.
Daily Accrual Example
Consider a $100,000 mortgage loan with a 15% APR accrued daily. Assuming the contract has a 365day year, as some are 360, the daily interest rate can be found by dividing 15% by 365. This calculation yields a daily interest rate of 0.0410958%.
The accrued interest on the first day of the mortgage is equal to $100,000 x 0.0410958%, or $41.0958. The account balance on day two equals $100,041.10 after rounding. Moving beyond day two, interest accrual depends on the compounding period.
Compounding Interest
Accrual and compounding periods are often different. Compounding changes the account balance from which the accrual calculations take place. If interest compounds monthly, then every month has a "compound date" where past accrued interest is summed and becomes the new base balance.
Take the previous $100,000 mortgage example. Under monthly compounding, the daily accrual amount, $41.0958, is the same for each day in the first month. On the compound date, all of the total accrued interest to that point is added to a new base amount. Every day in the second month uses the new, compounded loan balance.
Compounding can also take place daily or annually. Generally speaking, debtors are better off with less frequent accrual and compounding periods, while savers are better off with more frequent periods.

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