To induce fast payment by their buyers, many manufacturer offer cash discounts. An example of such an offer is: $1/10,$ n$/30.$ This example implies that the buyer will get a discount of $1\%$ on the purchase price if the bill is paid within $10$ days. If the buyer does not avail of this discount the bill must be paid within $30$ days. Assuming a buyer purchases good worth $10,713.$ She plans to pay for the goods and take advantage of the discount on the $10$th day. In order to do this, on the $10$th day she borrows the discounted amount from a bank and uses it to pay the manufacturer. The buyer will repay this loan to the bank after $20$ days. Effectively capturing the discount but delaying the payment for an additional $20$ days. Assume that the loan from the bank is compounded daily and that there are $365$ days in a year. What can be the highest Annual Percentage Rate $($APR$)$ compounded daily, charged by the bank, below which the buyer's plan of paying on the $10$th day rather than on the $30$th day makes financial sense? Enter your answer in decimal form to $3$ decimal places $($i$.$e$.$ if you want to answer $1\mathrm{.}234\%,$ enter $0\mathrm{.}012).$ If your answer is an exact midpoint you should round to the higher number. For instance, if your answer is exactly $23\mathrm{.}45\%,$ enter $0\mathrm{.}235.$