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What values do enter for N, PMT,i/y, FV and PV on a finance calculator to solve for the question below.

Derek decides to buy a new car. The dealership offers him a choice of paying $512.00 per month for 5 years (with the
first payment due next month) or paying some $28,300.00 today. He can borrow money from his bank to buy the car.
What interest rate makes him indifferent between the two options?

1 answer

To solve the given problem and find the interest rate (i/y) that makes Derek indifferent between paying $512.00 per month for 5 years or paying $28,300.00 today, we need to set up the cash flows and use the finance calculator appropriately.

Information Given:

  1. PMT (Payment per period): $512.00 (monthly payment)
  2. N (Total number of payments): 5 years × 12 months/year = 60 months
  3. PV (Present Value): This will be the amount today that we want to equate to the Present Value of the payment stream. The upfront payment is $28,300.00.
  4. FV (Future Value): Since it's an annuity and payments will cease after the last payment, we can set this to $0 (if not specified).
  5. i/y (Interest Rate): This is the unknown we are trying to find.

Values to Enter in the Finance Calculator:

  • N = 60 (total number of payments)
  • PMT = -512.00 (the payment is an outflow)
  • PV = 28,300.00 (present value, inflow)
  • FV = 0 (the value at the end of the last period)

Steps to find the interest rate (i/y):

  1. Set the calculator to the right mode (usually this should be in "End" mode since payments are made at the end of each period).
  2. Input the values into the calculator:
    • N = 60
    • PMT = -512.00
    • PV = 28,300.00
    • FV = 0
  3. Solve for i/y (Interest Rate).

Note:

  • Make sure to enter PMT as a negative value to reflect it as an outflow.
  • The result for i/y will give you the monthly interest rate, and you can multiply it by 12 to get the annual interest rate if needed.

Using a financial calculator or a financial software tool, you should be able to compute the interest rate that makes Derek indifferent between the two options.