On January $2,2023,$ Tim purchased a bond paying interest at $6\%$ for $$30,000.$ On March $31,2023,$ he gave the bond to Jane. The bond pays $$1,800$ interest on December $31.$ Tim and Jane are cash basis taxpayers. When Jane collects the interest in December $2023$:

a$.$ Jane must report $$1,800$ gross income.

b$.$ Jane reports $$1,350$ of interest income, and Tim reports $$450$ of interest income.

c$.$ Jane reports $$450$ of interest income, and Tim reports $$1,350$ of interest income.

d$.$ Tim must include all of the interest in his gross income.