A loan of $$11000$ is to be repaid by $10$

annual payments beginning $6$

months from the date of the loan. The first payment is to be half as large as the others. For the first $51/2$ years interest is at $0\mathrm{.}041$ effective; for the remainder of the term interest is at $0\mathrm{.}066$ effective. Find amount of the first payment.