A person borrows $15,000 and has to pay the sum back in 5 annual installments starting one year from the day at which the loan is made. The interest rates are compounded annually and are variable. The first two years, the interest rate is 10% per annum, the third year it is 12%, the fourth and fifth is 18%. What is the size of each annual installment? What is the amount of interest in each installment? What is the remaining principle after each installment?