Ralph Chase plans to sell a piece of property for $\$ 135000$. He wants the money to be paid off in two ways - a short-term note at $11 \%$ interest and a long-term note at $8 \%$ interest. Find the amount of each note if the total annual interest paid is $\$ 12900$.

Step 1 ：Let's denote the amount of the short-term note as x and the amount of the long-term note as y. We know that the total amount of the property is $135000, so we have the equation \(x + y = 135000\).

Step 2 ：We also know that the total annual interest paid is $12900, and the interest rates for the short-term and long-term notes are 11% and 8% respectively. So we have another equation \(0.11x + 0.08y = 12900\).

Step 3 ：We can solve these two equations to find the values of x and y.

Step 4 ：The solution to the system of equations gives us the amounts of the short-term and long-term notes. The short-term note is $70000 and the long-term note is $65000.

Step 5 ：This means Ralph Chase should sell the property with a short-term note of $70000 at 11% interest and a long-term note of $65000 at 8% interest. This will ensure that the total annual interest paid is $12900.

Step 6 ：Final Answer: The amount of the short-term note is \(\boxed{70000}\) and the amount of the long-term note is \(\boxed{65000}\).