How to Calculate the Number of Loan Payments with a Formula
A loan payment calculation tells you how many loan payments you need to make to pay off the loan in its entirety. This formula can also help you determine how many months you must continue to make loan payments if you pay off more than the required minimum loan payment each month. To determine the calculations, you need to know the total of the loan, the interest rate and the payment amount you plan to make each month. You also need to know how to calculate a logarithm or have a calculator with a "log" button and know how to use it.
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Instructions
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1
Divide the original amount of the loan by the loan payment. For example, if you had a $20,000 loan and were making payments of $500 per month, you would divide $20,000 by $500 to get 40.
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2
Multiply the number calculated in Step 1 by the interest rate per month on the loan. Normally, the interest given is yearly, so the yearly interest must be divided by 12. For example, a loan has an interest rate of 12 percent. That is equivalent to 0.12 in decimal form. Therefore, 0.12 divided by 12 equals 0.01. Then, 0.01 times 40 equals 0.4
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3
Calculate the negative log of the number calculated in Step 2. A log is also known as a logarithm. The log calculates the exponent of a number under a base 10. Use the log button on a calculator or the LOG function on a spreadsheet to calculate log. In the example, the negative log 0.4 equals 0.397940009.
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4
Add 1 to the interest rate per month. In the example, 0.01 plus 1 equals 1.01.
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5
Determine the log of the number calculated in Step 4. Follow the steps above to calculate the log. In the example, the log of 1.01 equals 0.004321374.
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6
Divide the number calculated in Step 3 by the number calculated in Step 5. In the example, 0.397940009 divided by 0.004321374 equals 92.08645877, which rounds to 93 months.
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References
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