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# Auto Cash Back vs Lower Rate Calculator

Cash Back with Higher Rate
Lower Interest Rate
%

months
%
Calculated Results
Cash Back is better if you pay off the loan before 22 months. Lower rate is better if you pay off the loan after 22 months
For Cash Back Offer
Loan Amount20467.5
Monthly Payment381.58
Total Interest2,425.63
Total Payment22,893.13
For Lower Rate Offer
Loan Amount21527.5
Monthly Payment367.99
Total Interest551.33
Total Payment22,078.83
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##### How to compare the cash back vs low interest rate auto loan
For cash back option, the buyer will have a lower total loan amount that will reduce the monthly payment and total interest payment. However, the interest rate for the auto loan will be normally higher than the low the same auto loan without cash back option. This interest rate difference could drive the total monthly payment up and offset the cash back you received in the long term. If you will pay off the auto loan early than the maturity date, most likely you will save on selecting the cash back option. On the other hand, if you will keep the loan to the maturity, you will mostly likely save on selecting the low interest rate option. Therefore, the calculator will calculate a breaking point for you. That is the number of months you should stay at the loan for the low interest rate option to edge over the cash back option.
Let's use an example to illustrate how the loan amount and interest rate impact the monthly payment.
For a 5 years loan with amount 20,000 and interest rate 6%, we can use the following formula to calculate monthly payment: $mp = Amount \frac{Rate(1+Rate)^{Term}}{(1+Rate)^{Term} - 1}$ Here Amount is the total loan amount, that is 20,000 in this case;
Rate is the monthly interest rate, that is 0.06/12 = 0.005;
Term is number of months to maturity date = 5x12 = 60.
If we plug in these values into the formula we will get monthly payment as 386.66.
Now if we reduce the loan amount by 1000 (means 1000 cash back), and keep the other values unchanged, then the calculated monthly payment is 367.32.
If we keep the loan amount, but reduce the interest rate to 3% (low interest rate), then the calculated monthly payment is 359.37.
If you only look the monthly payment, then the low interest rate is a better choice. However, if you have a plan to pay off your car loan before the maturity date, by just comparing the monthly payment is not enough because the total payoff amount is different in the two cases if the payoff happened before maturity date. Take an extreme case as an example, if you payoff the whole loan in the first month of the term, obviously, the cash back option is better than the low interest rate option. The calculator will calculate the break point as the number of months that you will stay at the loan by comparing the total payments that include both the monthly payment up to the pay off date and the total pay off amount.

##### New car incentives: Cash back vs low rates?

New-car incentives and rebates are used by automakers to either spur sales of slow-selling models or motivate a customer to stay loyal to the brand. They often take the form of cash discounts off the vehicle or low APR interest rates for financing.

Incentives and rebates can vary by region and often change from one month to the next. If you're in the market for a new car, be sure to compare the latest incentives being offered at dealerships in your area.

Here are the types of incentives you're most likely to come across when shopping for a new-car deal.

• Rebates/Customer Cash: These new car incentives are cash discounts taken off the listing price of the car. Buyers often must meet some requirements to get a rebate. Some rebates are only valid for recent college graduates, members of the military or a first responder.
• Low APR loan: This incentive offers low interest rates on financed vehicles, ranging from zero to about 5%. An eligible buyer's credit score needs to be fairly high. These promotional rates are often among the lowest available on the market. The low interest rates are sometimes tied to the length of the loan term, so pay attention to this detail. Low APR financing usually cannot be combined with customer cash.
• Lease Specials: Manufacturers often offer special lease programs through their captive financing companies. These are formally known as subvented or subsidized leases. These subsidized leases are generally based on a residual value that's much higher than the actual worth of the car at the end of the term.

In other words, the car makers and dealers adjust the residual value to bring down the monthly payment and thereby make their cars and trucks more appealing. When comparing car-buying incentives, it’s important to consider the financial factors and do the math so that you can make the right decision.

Some states do not tax the incentive rebates, while some other states do tax on them. The following states will NOT tax the incentive rebates: Alaska, Arizona, Delaware, Iowa, Kansas, Kentucky, Massachusetts, Minnesota, Missouri, Montana, Nebraska, New Hampshire, Oklahoma, Oregon, Pennsylvania, Rhode Island, Texas, Utah, Vermont and Wyoming