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I am trying to come up with the equation which will give me the total interest to be paid on something given a fixed interest rate with a fixed payment for a given period of time. The interest is applied to the remaining amount each month, after deducting any payments made.

I know how to work out the resulting total interest one month at a time, but I am unsure what the form of the equation would be given all of the known variables:

  • Total Due

  • Fixed Monthly Payment

  • Fixed Interest Rate (% of Remaining)

  • Number of Months

    = Total Interest

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Nathan Taylor
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2 Answers2

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I am trying to come up with the equation which will give me the total interest to be paid on something given a fixed interest rate with a fixed payment for a given period of time.

given all of the known variables:

  • Total Due
  • Fixed Monthly Payment
  • Fixed Interest Rate (% of Remaining)
  • Number of Months

Total Interest paid = (fixed monthly payment * number of months) - Initial balance

Example:

  • Total Due $20,000 for a car loan
  • Fixed Monthly Payment: $572.85
  • Fixed Interest Rate (% of Remaining) 2.0%
  • Number of Months 36 (3 years)

Total interest paid = (572.85 * 36)-20,000 = 20,622.66 -20,000 = 622.66

Using the mehod using Impt in Excel and summing the results $622.66

mhoran_psprep
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Because the payments go down over time, and you pay a different amount (in interest) each month, it's typically easier to generate an Amortization schedule and then add up the interest paid each month to arrive at the total interest paid.

There's a good article related to them here, as well as template you can use as a starting point. http://www.vertex42.com/ExcelArticles/amortization-calculation.html

NPFinance
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