How to Calculate Monthly Car Payments With Nominal Annual Interest Rate
As Stephen Kellison's discusses in "The Theory of Interest," the nominal rate, or stated rate, of a loan is the number of annual compounding periods times the periodic rate. If the nominal rate is 6 percent and interest is compounded monthly, then the periodic rate is 6/12 percent, or 0.5 percent. If you know the number of monthly payments total for the loan and the original loan amount, then you can figure out the monthly payment amounts using any calculator that can calculate exponents.
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Instructions
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Divide the nominal interest rate by 12, per the example given in the introduction. Denote it with the letter i.
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Determine the total number of monthly loan payments. For example, suppose the loan has a 5-year term. That's a total of 60 payments because 12 x 5 = 60 payments. Denote it with the letter N.
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Use your calculator to solve for (1+i)^N, where the caret ^ indicates exponentiation. Denote it with the letter X. Denote the original loan amount with the letter P and the monthly payments with the letter M.
For example, if i equals 0.5 percent and N is 60, then X = 1.3489.
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Solve for the monthly payment amount by calculating XPi / (X-1).
Continuing with the above example, for a total original loan amount of P = $15,000, you get M = 1.3489 x 15000 x 0.005 / 0.3489 = $289.96.
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Tips & Warnings
You can confirm your work in Microsoft Excel with the payment function. For the above example, the syntax is =PMT(0.005,60,15000). Note that the result is negative, because of the convention that outgoing is negative and incoming is positive.
Note that the above calculates the monthly payment toward interest and principal. It doesn't calculate any additional payment toward taxes or insurance.
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