Accrue means "increase in amount or value over time." If interest accrues on a bank account, you will have more money in your account. If interest accrues on a loan, you will owe more money to your lender.
Compound interest refers to interest earned on the total amount at the time it is compounded, including previously earned interest.
Continuous compounding refers to a loan or investment with interest that is compounded constantly, rather than on a specific schedule. It is equivalent to infinitely many but infinitely small compounding periods.
The principal is the amount of the original loan or original deposit.
The rate is the percentage at which interest accrues.
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Summary review of simple interest and exploration of continuously compounding interest