Robbie and Robin, both age $45,$ are married and filed a joint return for $2023.$ Robin earned a salary of $$100,000$ in $2023$ and is covered by her employer$$s $401($k$)$ plan. The employer made a $2\%$ nonelective contribution to the plan on her behalf in $2023.$ Robbie and Robin earned interest of $$40,000$ in $2023$ from a joint savings account. Robbie is not employed, and the couple had no other income. On April $15,2024,$ Robin contributed $$6,500$ to an IRA for herself and $$6,500$ to an IRA for Robbie. What is the maximum allowable IRA deduction on the $2023$ joint return? Please fully explain your answer.