Jia received $12,000 from a lottery. She uses this money to purchase two different annuities, each costing $6,000. The first annuity is a 24-year annuity-immediate paying $K per year, and the second is an 8-year annuity-immediate paying $2K per year. Both annuities are based on an annual effective interest rate of i, where i > 0. Determine K.