The formula for the principal amount of your car loan is (Purchase price) – (rebates) – (cash down payment) – (trade in value). A car purchase will also include fees and sales tax. Those two amounts are typically included in the principal amount. A rebate is a fixed amount of money paid to the buyer for the purchase of a particular vehicle. Rebates serve as an incentive to make the purchase. In most cases, the purchaser uses the rebate to reduce the principal amount of the loan. [2] X Research source A cash down payment is paid by the purchaser. You may also trade in a vehicle- usually the car you are replacing. A trade in is something you sell as partial payment for something new. In this case, the value of the car you trade in reduces the purchase price on the new vehicle. [3] X Research source Assume you’re buying a car for $20,000. The manufacturer provides a $2,000 rebate. You pay $3,000 as a down payment, and trade in a car valued at $5,000. The principal amount of your loan is $20,000 - $2,000 - $3,000 - $5,000, or $10,000.
Assume that your principal amount is $10,000. Your annual interest rate is 6%. You want to calculate the interest you owe for the month. Your interest rate for one month, also known as your monthly interest rate, is (6%/12 = 0. 5%).
When a loan is amortized, the borrower makes a fixed loan payment, usually monthly. That payment includes both repayment of principal and interest owed on the debt. As time goes on, each fixed loan payment includes a larger portion of principal repayment, and a smaller portion of interest. There are many amortization calculators on the Internet allow you to input a principal amount, loan term and interest rate. The calculator can provide the monthly payment, based on the criteria you input. Try searching online for “car loan calculator” to find one.
“M” represents your monthly payment. This is what the formula will be calculating. “P” represents your principal. As previously discussed, this is what you will pay for your car after rebates, trade-ins, and your down payment. “n” represents the total number of monthly payments over the life of the loan. So, if you have a standard, 6-year loan, this would be 6 six years * 12 months per year, or 72. i" represents your monthly interest rate. This is your stated interest rate, usually listed as your APR, divided by 12. So, if your stated interest rate is 6%, your monthly interest rate would be 6%/12, or 0. 5%. For the purpose of calculation, this number will have to be represented as a decimal instead of as a percentage. To get this number, simply divide your monthly percent interest by 100. In the example, this would be 0. 5%/100, or 0. 005.
For example, we can use the terms discussed previously. That is, a loan with $10,000 principal, 6% APR (interest), over 6 years. Our inputs would then be 10,000 for “P,” 0. 005 (the monthly interest rate, expressed as a decimal) for “i,” and 72 (6 years x 12 months per year) for “n. " Our example equation would now look as follows: M=10,000∗0. 005(1+0. 005)72(1+0. 005)72−1{\displaystyle M=10,000*{\frac {0. 005(1+0. 005)^{72}}{(1+0. 005)^{72}-1}}}
Start by solving the parts within the parentheses. In this case, this just means adding the 1 to the 0. 005 in both places. Your simplified equation should now look like this: M=10,000∗0. 005(1. 005)72(1. 005)72−1{\displaystyle M=10,000*{\frac {0. 005(1. 005)^{72}}{(1. 005)^{72}-1}}}
In our example, we raise 1. 005^72 and get 1. 432. Our equation now looks as follows: M=10,000∗0. 005(1. 432)(1. 432)−1{\displaystyle M=10,000*{\frac {0. 005(1. 432)}{(1. 432)-1}}}
After these calculations, our example equation will look as follows: M=10,000∗0. 00716)0. 432{\displaystyle M=10,000*{\frac {0. 00716)}{0. 432}}}
After this calculation, our sample equation will simply be M=10,000∗0. 0166{\displaystyle M=10,000*0. 0166}
Keep in mind that this number will vary slightly due to rounding during the calculation process.
In our example, this would be calculated as 72(“n”) * $166(“M”)=$11,952 - $10,000 (‘P”)= $1,952. So, total interest paid on this loan would be $1,952, which accounts for nearly one-fifth of the value of the loan.
