How the Cash Back Or Low Interest Calculator Works
Car makers often give buyers a choice: take a cash rebate, or take a special low interest rate on the loan, often as low as 0%, but not both. Both sound like good deals. Which one really saves you more money? The Cash Back or Low Interest Calculator works out the total cost of both choices on the same vehicle, so you can compare them fairly.
The two choices
- Choice 1: take the cash back. The rebate lowers the price, so you borrow less. But you use your own loan, from your bank or credit union, at a normal rate.
- Choice 2: take the low-rate loan. You give up the rebate. You borrow more, but the interest on it is much lower.
What you enter
- Vehicle price, down payment and trade-in: the same for both choices.
- Sales tax: the rate, and whether it is charged on the full price or on the price after the cash back. This depends on where you live.
- Cash back: the rebate, in dollars.
- Your own loan: the rate and term you can get from your bank or credit union.
- The low-rate offer: its rate and term.
How each choice is worked out
amount borrowed = price - cash back (choice 1 only) + sales tax - down payment - trade-in monthly payment = P x r x (1 + r)^n / ((1 + r)^n - 1) total you pay = monthly payment x number of months
In the payment formula, P is the amount borrowed, r is the monthly rate (the yearly rate divided by 12) and n is the number of months. The down payment and trade-in are the same for both choices, so comparing the totals of the payments compares the whole cost.
A worked example
A vehicle costs $35,000. You put $3,000 down. There is a $3,000 cash rebate, or a 1.9% loan for 60 months. Sales tax is 7% of the full price, which is $2,450. Your own bank would lend at 6.5% for 60 months.
| Cash back and your own loan | Low-rate loan | |
|---|---|---|
| Amount borrowed | $31,450.00 | $34,450.00 |
| Interest rate | 6.5% | 1.9% |
| Monthly payment | $615.36 | $602.33 |
| Total of the payments | $36,921.32 | $36,139.53 |
Here the low-rate loan is better. It costs $781.80 less in all, and the monthly payment is lower too. The rebate of $3,000 is not big enough to make up for the difference in interest.
Chart: what you pay in total
The dark blocks are the money you borrow, and the light blocks are the interest:
Cash back and own loan ██████████████████████████████████░░░░░░ $36,921 Low-rate loan █████████████████████████████████████░░ $36,140
The break-even rate
The most useful number is the break-even rate. It is the rate on your own loan at which the two choices cost exactly the same. In the example, it is 5.61%. If your bank or credit union offers you less than 5.61%, take the cash back. If it offers more, take the low-rate loan.
| Your own loan rate | Total with cash back | Total with the low rate | Better |
|---|---|---|---|
| 4.5% | $35,179 | $36,140 | Cash back |
| 5.5% | $36,044 | $36,140 | Cash back |
| 6.5% | $36,921 | $36,140 | Low rate |
| 7.5% | $37,812 | $36,140 | Low rate |
| 8.5% | $38,715 | $36,140 | Low rate |
At a 3% loan of your own, the cash back would win by $2,232.61.
When each choice tends to win
- The low rate tends to win when the loan is large, the term is long, or your own rate would be high.
- The cash back tends to win when the rebate is big, the loan is short, or you can get a low rate on your own, for example from a credit union, or if you have excellent credit.
- Paying cash makes the cash back the clear winner, because there is no interest to save.
Tips
- Get a pre-approved loan offer from a bank or credit union before you visit the dealer. It gives you the number to enter.
- Check the terms of the low-rate loan. The special rates are often for shorter terms and for buyers with top credit.
- Compare the monthly payment too. A shorter term has a higher payment, which may not fit your budget.
- Ask if you can take both. Sometimes a dealer allows part of the rebate with a low rate.
What this calculator does not include
- Fees, add-ons, insurance and any early payment penalty on either loan.
- Differences in the rules for how sales tax treats a rebate. Choose the option that applies to you.
- The chance to pay the loan off early, which lowers the interest on both choices.
This tool gives an estimate for general information only. It is not financial advice. The dealer's offer and your lender's loan agreement have the exact terms.