A man has just won the lottery and received a prize of $200,000 after tax. He decides to purchase a new home at a price of $400,000. According to the home loan that he would like to apply for, the initial principal he has to repay is 20% of the property price. The remaining principal will be repaid via 8 years' monthly payments. The payments are currently at the level of $X at the end of each month, which is enough to have the property paid off exactly in 8 years at the current interest rate of 4.5% p.a. effective. Find $X.