I know that when the Federal Reserve buys Treasury bonds it increases the money supply, but I don't understand the process behind it. The model that I have given below (which is my best understanding of open market operations) is wrong and I need help understanding why.
Suppose the US Government through the Treasury issues a \$100 bond with a yield of \$110. A third party purchases the bond and later sells it to the Federal Reserve for $105 during open market operations. Before the maturity date, the balance of the US Government is \$100, third party \$5, and Federal Reserve -\$105. At the maturity date, the balance of the US Government is -\$10, third party \$5, and Federal Reserve \$5.
This model erroneously depicts a zero sum transaction and not an increase in the money supply.