Aiden commits to a mortgage with an interest rate of $5\%$ compounded semiannually for the first thirteen years and $2\%$ compounded annually for the next ten years. He pays $$11451$ at the beginning of every semi$-$annual period. How much was the original listing price on the house he purchased?

Today

$13$ years

$23$ years

Calculate the following values on the time diagram.

$PV1=$$

The original listing price on the house was $