Diggs is a $47-$year$-$old executive who earns $$315,000$ from his job at Acme Arrows $($AA$)$ and contributes the maximum amount to the AA $401($k$)$ plan. He wants to make a contribution to a Roth IRA for the current year, but his compensation is over the income limit$.$ He decides he wants to fund a Roth IRA by using the backdoor Roth technique. Assume that Diggs has a traditional IRA with a balance of $$24,000$ that was funded entirely with pre$-$tax contributions. If Diggs contributes $$7,000$ to a traditional IRA and then converts $$7,000$ to a Roth IRA, how much income will he have to pick up as a result of the conversion?

Question $5$ options:

$$0$

$$5,419$

$$7,000$

$$1,580$