A store will give you a 2.00% 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

The implicit borrowing rate is 27.43% per year.

Explanation:

We are told that the store will give a 2% discount on the cost of purchase if cash was paid today.

This means that for example, if the cost price of the items is maybe $200, then the price you have to pay at that moment is $196.

We are told that if you want to pay within a month, you will pay full cost.

Thus, if the cost is still $200, it means you will pay $200 at the end of 1 month.

Now, if we compare how much you will pay at the end of one month as against if you will pay immediately, you will see that'll there's a difference of $200 - $196 = $4

This means an increase of: (4/196) × 200% = 2.04%

Note that this is just the increase to get back to original cost of $ 200.

Now if we compound these interests, it will mean that in a year you have to pay the interests each month on an amount of money that's steadily growing.

Now, since there are 12 months in a year, the implicit borrowing rate at the end of 1 year will be;

([(200/196)^(12)] - 1) × 100% = 27.43%

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