A man wishes to borrow 1000$. One lender offers a loan in which the principal is to be repaid at the end of four years. In the meantime j = 4.5% effective is to be paid on the loan and the borrower is to accumulate the principal by means of a sinking fund earning i = 4% effective. Another lender offers a loan for four years in which the borrower repays the principal by the amortization method. What is the largest rate of interest that this lender can charge so that the borrower is indifferent between the two offers?