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Scenario 1: Find the Amount of Payment

Loan Amount (C)

Interest Rate % (R)

Compound Frequency (m)

No. of Payments (N)

Payment Frequency (q)

Payment Amount (P): 
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

Loan Amount (C)

Payment Amount (P)

No. of Payments (N)

Payment Frequency (q)

Compound Frequency (m)

Interest Rate % (R): 
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

Loan Amount (C)

Interest Rate % (R)

Compound Frequency (m)

Payment Amount (P)

Payment Frequency (q)

No. of Payments (N): 
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.