Auto Loan Calculator

Car Price ($):

Cash Available ($):

Trade-In Value ($):

Sales Tax Rate (%):

Annual Interest Rate (%):

Loan Term (Months):

1. What is the Auto Loan Calculator?

Definition: The Auto Loan Calculator computes the monthly payment and total interest cost for a car loan, accounting for the loan amount, interest rate, and loan term. The loan amount is determined by the car price, cash available, trade-in value, and sales tax.

Purpose: This tool helps individuals plan car purchases by estimating affordable monthly payments and understanding the total cost of borrowing, aiding in budgeting and financial decision-making.

2. How Does the Calculator Work?

The calculator uses the following formulas:

$ L = P - C - (T \times (1 - S)) $

$ M = L \times \frac{R_m}{1 - (1 + R_m)^{-T_m}} $

$ I = (M \times T_m) - L $

Where:

$ L $: Loan amount;
$ P $: Car price;
$ C $: Cash available;
$ T $: Trade-in value;
$ S $: Sales tax rate;
$ M $: Monthly payment;
$ R_m $: Monthly interest rate ($ R / 12 $, where $ R $ is annual interest rate);
$ T_m $: Loan term (months);
$ I $: Total interest cost.

Steps:

Enter the car price, cash available, trade-in value, sales tax rate, annual interest rate, and loan term.
Calculate the loan amount by subtracting cash and after-tax trade-in value from the car price.
Compute the monthly payment using the loan amount, monthly interest rate, and loan term.
Calculate total interest by multiplying monthly payment by loan term and subtracting the loan amount.
Display results in currency format with two decimal places.

3. Importance of the Auto Loan Calculation

Calculating auto loan payments is essential for:

Budgeting: Ensures monthly payments fit within your financial plan, preventing overextension.
Cost Transparency: Reveals the total interest cost, helping compare loan offers and make informed decisions.
Trade-In Planning: Accounts for trade-in value and sales tax, optimizing the loan amount needed.

4. Using the Calculator

Example: Calculate the loan for a $20,000 car, with $1,500 cash, $7,000 trade-in value, 10% sales tax, 4% interest rate, and 36-month term:

Trade-In After Tax: $ 7,000 \times (1 - 0.10) = 6,300 $;
Loan Amount: $ 20,000 - 1,500 - 6,300 = 12,200 $;
Monthly Rate: $ 0.04 / 12 = 0.003333 $;
Monthly Payment: $ 12,200 \times \frac{0.003333}{1 - (1 + 0.003333)^{-36}} = 360.19 $;
Total Interest: $ 360.19 \times 36 - 12,200 = 766.84 $;
Result: Monthly Payment: $360.19; Total Interest: $766.84.

5. Frequently Asked Questions (FAQ)

Q: What is an auto loan?
A: An auto loan is a loan used to purchase a vehicle, repaid in monthly installments with interest over a set term.

Q: How does sales tax affect the loan?
A: Sales tax reduces the net trade-in value, increasing the loan amount needed if not covered by cash or trade-in.

Q: Can I lower my monthly payment?
A: Yes, by increasing cash down payment, trading in a higher-value car, choosing a lower interest rate, or extending the loan term (though this increases total interest).