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Part A: What is the approximate APR formula?

Part A: What is the approximate APR formula?
Part B: Keely buys a car for $18,000 with a down payment of $1,000. Estimate her APR to the nearest tenth of a percent if her monthly payments are $375 per month for 60 months.
Part C: Show your work to support your answer to Part B.

Answer

Part A: The approximate APR formula is:
APR ≈ 2 * n * I / (P * (n + 1))
where n is the number of payments per year, I is the total interest paid over the life of the loan, and P is the principal amount of the loan.

Part B: The principal amount financed is $17,000 ($18,000 - $1,000). The total amount paid over 60 months is $375 * 60 = $22,500. The total interest paid is $22,500 - $17,000 = $5,500. Using the approximate APR formula:
APR ≈ 2 * 12 * 5500 / (17000 * (60 + 1)) ≈ 0.065 or 6.5%

Part C:

  1. Calculate the principal amount financed: $18,000 - $1,000 = $17,000.
  2. Calculate the total amount paid: $375 * 60 = $22,500.
  3. Calculate the total interest paid: $22,500 - $17,000 = $5,500.
  4. Use the approximate APR formula: APR ≈ 2 * 12 * 5500 / (17000 * (60 + 1)) ≈ 0.065 or 6.5%.

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