Annuity Payments Ford Motor Company’s Current Incentives Inc

Annuity Payments Ford Motor Companys Current Incentives Include

Ford Motor Company's current incentives include 5.7 percent APR financing for 72 months or $1,100 cash back on a Mustang. Suzie Student is interested in purchasing the premium Mustang convertible, which has a listed price of $34,000. She has no down payment other than the cash back from Ford. Thus, she has two options:

  • Accept the $1,100 cash back and finance the remaining amount at her credit union, or
  • Use the cash back as a down payment and finance the rest at Ford's promotional 5.7% APR rate.

First, let's analyze the financing options in detail. If Suzie opts for the $1,100 cash back, she will borrow $32,900 from the VTech Credit Union at APR 7.7% for 72 months. Her monthly payment can be calculated using the standard amortization formula for an annuity:

PMT = (P × r) / (1 - (1 + r)^-n)

Where:

  • P = principal amount borrowed = $32,900
  • r = monthly interest rate = annual rate / 12 = 7.7% / 12 = 0.077 / 12 ≈ 0.006417
  • n = total number of payments = 72

Calculating the monthly payment:

PMT = (32900 × 0.006417) / (1 - (1 + 0.006417)^-72)

PMT = 211.026 / (1 - (1.006417)^-72)

Calculating (1.006417)^-72:

(1.006417)^-72 ≈ 0.6358

Then, denominator: 1 - 0.6358 = 0.3642

Finally, monthly payment: PMT ≈ 211.026 / 0.3642 ≈ $579.56

Therefore, Suzie's monthly payment if she finances $32,900 at 7.7% over 72 months is approximately $579.56.

Next, let's determine the monthly payment if she opts for the 5.7% APR financing directly from Ford for the full $34,000:

Using the same amortization formula with:

  • P = $34,000
  • r = 5.7% / 12 = 0.057 / 12 ≈ 0.00475
  • n = 72

Calculating the monthly payment:

PMT = (34000 × 0.00475) / (1 - (1 + 0.00475)^-72)

PMT = 161.5 / (1 - (1.00475)^-72)

Calculating (1.00475)^-72 ≈ 0.6951

Denominator: 1 - 0.6951 = 0.3049

Monthly payment: PMT ≈ 161.5 / 0.3049 ≈ $530.02

Hence, her monthly payment at the 5.7% APR financing is approximately $530.02.

Which option should Suzie Student choose?

Comparing the two options:

  • Finance $32,900 at 7.7% APR: approximately $579.56/month
  • Finance $34,000 at 5.7% APR: approximately $530.02/month

While the monthly payment at the lower interest rate is smaller, it's important to recognize that the total amount paid over the life of the loan is higher in the first scenario, since she is financing a larger amount. Additionally, accepting the $1,100 cash back and borrowing at the higher rate results in higher total interest expenses.

The better financial decision depends on Suzie's cash flow preferences. The lower monthly payment at 5.7% APR makes monthly budgeting easier and saves her money over the lifetime of the loan compared to financing the full amount at 7.7%. However, if she prefers to keep her immediate cash on hand and can handle the slightly higher monthly payments, financing the smaller amount ($32,900) at her credit union's rate is advantageous.

Overall, given the lower monthly payment and total cost, Suzie should opt for Ford's 5.7% APR financing for the full $34,000, provided she is comfortable with the monthly payments of approximately $530.02, which are lower than the $579.56 she would pay borrowing at 7.7%. This option minimizes her total interest expense and simplifies her financing decision.

References

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  • Celuch, K., & Murphy, P. (2018). Consumer Financing and Loan Decision-Making. Journal of Consumer Research, 45(3), 502-520.
  • Dunn, J., & Cheatham, J. (2020). Personal Finance. McGraw-Hill Education.
  • Investopedia. (2023). Understanding Loan Payments and Amortization. https://www.investopedia.com
  • Kapoor, J. R., Dlabay, L. R., & Hughes, R. J. (2015). Personal Finance (11th ed.). McGraw-Hill Education.
  • Ross, S. A., Westerfield, R. W., & Jaffe, J. (2013). Corporate Finance (10th ed.). McGraw-Hill Education.
  • SmartAsset. (2023). How to Calculate Loan Payments. https://smartasset.com
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  • U.S. Federal Reserve. (2023). Consumer Credit and Household Debt. https://federalreserve.gov

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