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Shellie, a single individual, received her bachelor's degree in $2022$ and took a job with a salary of $$45,000$ per year. In $2023,$ she paid $$1,500$ of interest on qualified education loans. Which of the following statements is true?

a$.$ The full $$1,500$ is deductible in arriving at adjusted gross income $($AGI$).$

b$.$ If her income had been $$70,000,$ the deductible amount would have been phased out.

c$.$ She is not allowed a deduction for education loan interest in $2023.$

d$.$ If her payment had been $$3,000,$ only $$2,000$ would have been deductible in arriving at AGI and the $$1,000$ excess would have been treated as nondeductible consumer interest.