What mortgage calculation equation do I use to calculate my monthly amortization payments?

Use the following mortgage calculation equation to compute your monthly amortization payments.  Note that this mortgage calculation formula assumes that your interest rate is fixed and interest is compounded monthly.

The mortgage calculation equation:

A=MP x {[MIR x (1 + MIR) ^m] ÷ [(1 + MIR) ^m - 1]}

Where:

• A =  your monthly amortization payment
• MP = your mortgage principal
• MIR = your monthly interest rate
• m = the number of months you've left to make payments

Clearly, you need to do some derivations before you can start using the above mortgage calculation equation.  Specifically, you need to compute your monthly interest rate (MIR) and the number of months you will have to make monthly mortgage payments (m).

Compute your monthly interest rate (MIR):

1. Determine your annual rate of interest.
   Ex: 6 percent
2. Divide that annual rate by 12 months.
   Ex: 0.06 / 12 = 0.005

Compute the number of months you'll make amortization payments (m):

1. Determine the number of years you have to pay off your mortgage.
   Ex: 20 years
2. Multiply this by 12.
   Ex: 20 x 12 = 240 months

Now that you have derived both your monthly interest rate (MIR) and the number of months you have to pay off your mortgage (m), use the mortgage calculation equation to compute your monthly amortization.

Compute your monthly amortization using the mortgage calculation equation:

Let's suppose that your principal is $150,000. For the rest of the variables, let's use the values we've derived earlier.

A=MP x {[MIR x (1 + MIR) ^m] ÷ [(1 + MIR) ^m - 1]}

Where:

• MP = $150,000 (your principal)
• MIR = 0.005 (your monthly interest rate)
• m = 240 (the number of months you have to pay)

Therefore:

A = $150,000 x {[0.005 x (1 + 0.005)²⁴⁰] / [(1+0.005)²⁴⁰ - 1]}

A = $150,000 x {[0.005 x (1.005)²⁴⁰] / [(1.005)²⁴⁰ - 1]}

A = $150,000 x 0.0071643105847816487734026559526033

A = 1074.6465877172473160103983928905

A = $1,074.65

Result:

According to the mortgage calculation equation, you need to make monthly amortization payments of $1,074.65 in order to pay off a $150,000 mortgage with a 6% interest rate per annum in 20 years.

Notes:

*This result was derived using exact values.  Rounding off anywhere in your computation will give you a slightly higher or lower figure.

**(1.005) ²⁴⁰ = 3.3102044758074479319626995622572.  You can calculate this by using the x^y key in your scientific calculator or the Power function in MS Excel.

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