How to Calculate Payments With Amortized Interest

If you're a savvy borrower, you understand that each time you make a payment on a loan, you reduce the amount of principal you still owe, which, in turn, reduces the interest-bearing balance. Although calculating the amount you owe after each payment can be mathematically tedious, it can help save you large amounts of interest on a long-term loan. Fortunately, you can create an amortization schedule that normalizes your interest over the life of the loan and calculates the amount of each monthly payment you need to make on that schedule.

• 1

  Define the life of the amortization schedule by the number of scheduled payments. For example, a five-year loan with monthly payments would have 60 payment periods. Set this number as variable n. This example will calculate the payments on a five-year, 5 percent loan of $10,000. So n = 60 in this example.

• 2

  Define your interest rate. If your loan has variable interest rates, you'll need to develop an amortization schedule for each interest rate. Change an annual interest rate to a monthly interest rate, expressed as a decimal. This is variable i. Thus, a 5 percent interest rate would be an interest rate of 0.0041 monthly (0.05/12). So i = 0.0041.

• 3

  Define variable p as the principal amount borrowed. The principal borrowed in the example is $10,000, so p = 10,000.

• 4

  Calculate the monthly payment amount, variable a, by plugging your variables into the following formula:

  a = p x [ (i [1+ i]^n)/([1+i]^n -- 1)]

  ^ n means raised to the power of n

  Using figures provided in the example, the equation is written as:

  a = 10,000 x [(0.0041 x [1 + 0.0041] ^ - 60)/([1+0.0041)^60 - 1)]

  The calculation simplified is:

  a = 10,000 x [(0.0041 x 1.0041^60)/(1.0041^60 -- 1)

  a = 10,000 x (0.0041 x 1.278)/(1.278 -- 1)

  a = 10,000 x (0.0052)/.278

  a = 10,000 x 0.019

  a = 190.00

  a = $190.00