Amortization calculator

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An amortization calculator is used to determine the periodic payment amount due on a loan (typically a mortgage), based on the amortization process.

The amortization repayment model factors varying amounts of both interest and principal into every installment, though the total amount of each payment is the same.

An amortization calculator can also reveal the exact dollar amount that goes towards interest and the exact dollar amount that goes towards principal out of each individual payment. The amortization schedule is a table delineating these figures across the duration of the loan in chronological order.

[edit] The Formula

The calculation used to arrive at the periodic payment amount assumes that the first payment is not due on the first day of the loan, but rather one full payment period into the loan.

While normally used to solve for A, it can be used to solve for any single variable in the equation provided that all other variables are known.

The formula is:

A \;= \;P\;\frac{i(1 + i)^n}{(1 + i)^n - 1} \;= \frac{P i}{1 - (1 + i)^{-n}}

Where:

A = periodic payment amount

P = amount of principal (be sure to subtract any down-payments first!)

i = periodic interest rate

n = total number of payments (for a 30-year loan with monthly payments, n = 30 years x 12 months = 360)

Note that the interest rate is commonly referred to as an annual percent (e.g. 8% APR), but in the above formula, since the payments are monthly, the rate i must be in terms of a monthly percent. Given interest originally in terms of an annual percent, obviously, just divide by 12.

[edit] Other uses

While often used for mortgage-related purposes, an amortization calculator can also be used to analyze other debt, including short-term loans, student loans and credit cards.

where P=current balance, i=card's interest rate, and n=12.

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