Question

A store will give you a 4.75% discount on the cost of your purchase if you pay cash today. Otherwise, you will be billed the full price with payment due in 1 month. What is the implicit borrowing rate being paid by customers who choose to defer payment for the month? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

Annual effective rate is 79.38%

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Assume that the cost of purchase was $1oo. The discount of 4.75% will be available if the payment was made today.

Calculate the price paid today after receiving discount as follows:

Net amount paid = 100 – (100* 0.0475)

                             = 100 – 4.75

                              = 95.25

Monthly rate = Discount/ cost

                       = 4.75/ 95.25

                       = 0.049868 or 4.99% per month

Now we need to find the annual effective interest rate

Effective interest rate = (1 + i/m) ^m -1

Where,

Nominal interest rate (i) = 59.88% per year

Number of compounding in a year (m) = 12

Let's put all the values in the formula

Effective interest rate = (1 + 0.5988/12) ^12 - 1

                                              = (1 + 0.0499) ^12 - 1

                                              = (1.0499) ^12 - 1

                                              = 1.7938 - 1

                                              = 0.7938

So annual effective interest rate is 79.38% per year

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