A price level adjusted mortgage $($PLAM$)$ is made with the following terms, to be adjusted

by the CPI after year $1$:

$$ Amount $=$ $$125,000$

$$ Initial Interest Rate $=5\%$ monthly compounded

$$ Term $=30$ years

$$ CPI during year $1=8\%($increase$)$

What is the balance at the end of the first year?

A$)$ $$125,000$

B$)$ $$123,155$

C$)$ $$133,008$