Amortized Loans

The following formulas concern loans that follow a repayment schedule such that the nominal repayment amount is constant in each period for the duration of the loan's timeframe (e.g. mortgages, student loans).

• Per-period Payment
• Early Payment/Refinance

Per-period Payment

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The per-period payment amount (C) on the borrowed principal (P) must satisfy:

Borrowed principal (P)

APR

# periods/year (k)

# periods (N)

Calculate

C=

Early Payment/Refinance

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This formula represents the outstanding principal amount of an amortized loan at period (n):

Per-period payment (C)

APR

# periods/year (k)

# periods (N)

Period of interest (n)

Calculate

(t=n) P=