a) You took out a one-year loan for $1000 and agreed to pay it in three equal installments, one payment at the end of 1 month, second payment at the end of 2 months, and the last payment at the end of the year. What is the size of each payment? Assume the interest rate is 9%.

b) In part (a), suppose that you made three non-equal payments: the first was $500 at the end of 1 month, the second was $900 at the end of 2 months and the final payment was $X at the end of the year. What is the value of X if the interest rate is 8%? Use the declining balance method.