Melvin receives $640,000 at his retirement. He invests $X in a 20-year annuity- immediate with level annual payments and the remaining $640,000 - X is used to purchase a perpetuity-immediate with level annual payments. The total annual payments received during the first twenty years are twice as large as those received thereafter. If the nominal annual interest rate is 3% compounded monthly, deter- mine the value of X. Please use actuary notation not excel notation.