If an annuity is for repaying a debt P with interest, the amount owed after n payments is:
because the scheme is equivalent with borrowing the amount to create a perpetuity with coupon, and putting of that borrowed amount in the bank to grow with interest . Conceptually, the payments to the perpetuity are being applied against an amount of of the debt, while the additional debt of compounds until retired in a single payment from the saved amount. What remains owed after the obligation to the excess borrowing is retired is the amortized amount of debt due to borrowing .
Also, this can be thought of as the present value of the remaining payments:
See also fixed rate mortgage.
Read more about this topic: Annuity (finance Theory)
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