Your monthly car payment depends on the amount borrowed, the interest rate and the length of the loan. Entering these key variables in the following annuity formula calculates what car payment you can expect, assuming you don't make extra payments or incur late fees for untimely payments:
PMT = $10,000 * (r / 12) / (1 - (1 + r / 12) ^ (-12 * n))
Where PMT is the monthly car payment, r is the annual interest rate and n is the length of the loan in years. This rather complicated formula is better understood by walking through an example. For this example, assume you have a $20,000 loan with a 6 percent annual interest rate for five years.
Use the actual loan amount in this calculation, rather than the cost of the car. These figures might be different if you made a down payment or traded in a vehicle when purchasing the car.
Step 1: Calculate the Monthly Interest Rate
Divide the annual interest rate by 12 to convert it to a monthly rate. The result takes the place of "r/12" in the formula. In the example, divide 6 percent by 12 to calculate a monthly rate of 0.5 percent, or 0.005.
Step 2: Calculate the Number of Payments
Multiply the number of years by 12 to calculate the number of payments. For use in the formula, however, this number should be negative, so multiply by negative 12. This calculation takes the place of "-12*n" in the formula. In the example, multiply 5 by -12 to get -60.
Step 3: Calculate the Divisor
Add 1 to the monthly rate, raise the result to the number you just calculated and then subtract the result from 1. In the example, add 1 to 0.005 and raise the resulting 1.005 to the power of -60 to get 0.7414. Subtract this figure from 1 to get 0.2586.
Step 4: Calculate the Multiplier
Divide the monthly rate by the divisor. In the example, divide 0.005 by 0.2586 to get 0.0193. This figure is the fraction of your original loan you pay each month to pay off the loan in the allotted time.
Step 5: Calculate the Monthly Payment
Multiply the loan amount by the multiplier to calculate the monthly payment. In the example, multiply $20,000 by 0.0193 to get a monthly payment of $386.
If you already have budgeted a monthly car payment, divide the multiplier into this figure to calculate the loan amount that results in that payment. In the example, if you budgeted $500 for a car, divide $500 by 0.0193 to calculate the maximum loan amount of $25,907 that fits your budget, assuming the interest rate remains the same.