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, (the payment, given the terms) it can be used to solve for any single variable in the equation provided that all other variables are known. One can rearrange the formula to solve for any one term, except for i, for which one can use a root-finding algorithm.
The annuity formula is:
Where:
- A = periodic payment amount
- P = amount of principal, net of initial payments, meaning "subtract any down-payments"
- i = periodic interest rate
- n = total number of payments
This formula is valid if i > 0. If i = 0 then simply A = P / n.
- For a 30-year loan with monthly payments,
Note that the interest rate is commonly referred to as an annual percentage rate (e.g. 8% APR), but in the above formula, since the payments are monthly, the rate must be in terms of a monthly percent. Converting an annual interest rate (that is to say, annual percentage yield or APY) to the monthly rate is not as simple as dividing by 12, see the formula and discussion in APR. However if the rate is stated in terms of "APR" and not "annual interest rate", then dividing by 12 is an appropriate means of determining the monthly interest rate.
Read more about this topic: Amortization Calculator
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