# Leslie has been offered the choice of either a $1,000 rebate or a 5.5%, 48-month loan for the new... ## Question: Leslie has been offered the choice of either a$1,000 rebate or a 5.5%, 48-month loan for the new car she is purchasing.

If Leslie will be financing $15,000 and she can get a 7.5%, 48-month loan at her credit union, should she take the$1,000 rebate or the 5.5% loan?

## Cash Rebate or Lower Interest:

Car dealers often offer incentives in one of two forms: a cash rebate or a lower interest rate on loans. When deciding which option to take, consumers need to consider factors such as the price of the car, and the cost of credit the consumer can secure elsewhere.

She should take the rebate.

To decide which one to take, we can compute the monthly payment under each plan, and the plan with a lower monthly payment should be chosen. We can use the following formula to compute the monthly payment for a loan with principal {eq}P {/eq}, monthly interest rate {eq}r{/eq} and number of monthly payments {eq}T{/eq}:

• {eq}\displaystyle \frac{Pr}{1 - (1 + r)^{-T}} {/eq}

If she chooses the rebate, the amount borrowed will be 15,000 - 1,000 = 14,000. The monthly interest rate is 7.5%/12, and there are 48 payments. Applying the formula, the monthly payment is:

• {eq}\displaystyle \frac{14,000*7.5\%/12}{1 - (1 + 7.5\%/12)^{-48}} = 338.50 {/eq}

If she chooses the loan, the amount borrowed will be 15,000, the monthly interest rate is 5.5%/12, and there are also 48 payments. The monthly payment is:

• {eq}\displaystyle \frac{15,000*5.5\%/12}{1 - (1 + 5.5\%/12)^{-48}} = 348.85 {/eq}

Since the first option has a lower monthly payment, it should be chosen.