Early settlement discounts

Formula in Study Text:
Annual cost of discount = (1 + discount/amount left to pay) no. of periods -1

A company is offering a cash discount of 2.5% to receivables if they agree to pay debts within 1 month. The usual credit period taken is 3 months.

What is the effective annualised cost of offering the discount and should it be offered, if the bank would loan the company at 18% p.a.?

My workings:
I assumed an invoice of $100.

(1 + 2.50/97.50) to the power of 6 (12/2) – 1= 16.405% and I rounded it to 16.41%
Yes, it wise to offer the settlement discount.

The answer in the Study Text was 16.38%.

Where did I go wrong?

Thanks! 🙂