Selected pension data for Rotman Company for $2018$ were as follows: PBO, January $1,$ $$240,000$ and December $31,$ $$270,000$; pension plan assets $($fair value$)$ January $1,$ $$180,000,$ and December $31,$ $$230,000.$ The projected benefit obligation was underfunded at the end of $2018$ by:

Group of answer choices

$$30,000.$

$$60,000.$

$$20,000.$

$$40,000.$