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From what I understand, effective date is another word for disbursement date and initial date is when payments will be made.

Sometimes the dates are the same then no extra cases need to be made. If the dates are different, how do I calculate the interest that accrues? Does it play a role with loan amortizations, payments, or balance?

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I know that when I close on a mortgage there's the issue that requires me to pay interest up front, i.e. interest to take me to the end of current month, so the mortgage starts on the 1st and them runs 15/30 years from there. This may produce the two dates you're asking about.

The partial month interest is simple, in both senses. The mortgage then amortizes over the term.

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