Calculating Equivalent Annual Cost of Discount

Hi Sir, Came across this question in the kaplan study text. I was unable to understand the solution provided by the book, would appreciate if the solution is simplified and explained in detail especially the step 2 & 3. The question and the solution provided by the Book is below Q) Work out the equivalent annual cost of the following credit terms. 1.75% discount for payments within 3 weeks. Alternatively, full payment must be made within 8 weeks of the invoice date. Assume there are 50 weeks in a year. Hint, consider a $100 invoice. A) Step 1 - Work out the discount available and the amount due if the discount were taken. Discount available on; $100 invoice = 1.75%*100 = 1.75 dollars. Amount due after discount is; 100*1.75 = 98.25. Step 2 - the effective interest rate cost of not taking the discount is; 1.75 / 98.25 = 0.0178 for an 8-3 = 5 week period. Step 3 - calculate the equivalent annual rate. There are 10, 5-week periods in a year. The equivalent interest rate is; ((1 + 0.18) ^ 10)- 1 = 0.195 or 19.5%