|Scenario 1: Find the Amount of Payment|
Interest rate R% is always a yearly figure. However, in most loan situations it is compounded monthly. In this calculator
the Payment Amount P is calculated by the following formula
where r is the adjusted equivalent interest rate
For most loans, interests are compounded monthly and payments are also made monthly (m=q=12). r is then simplified to R/1200:
Note that the number 100 is to convert the percentage value R% to decimal.
|Scenario 2: Find the Interest Rate|
For given C, P and N, one can only solve the following equation for r by numerical means.
Given the rather smooth behavior of this equation, this calculator employs the Newton-Raphson method with an educated initial guess:
The annual interest rate R% is
|Scenario 3: Find the Number of Payments|
This calculator figures out the Number of Payments N by the following closed-form expression:
Notice that N has to be an integer, so the Payment Amount P might be slightly adjusted to satisfy this condition.