A loan of P is to be repaid by 10 annual payments starting 6 months from the date of the loan. The first payment is to be half as large as the...

A loan of P is to be repaid by 10 annual payments starting 6 months from the date of the loan. The first payment is to be half as large as the others. For the first 4.5 years interest is at i effective; for the remainder of the term interest is at j effective. Find an expression for the first payment.