Final answer:
Roger, at 73 years of age, can contribute up to $7,000 to a traditional IRA or Roth IRA in 2021, which includes a $1,000 catch-up contribution for people over 50.
Step-by-step explanation:
In 2021, Roger, who is 73 years old with a modified adjusted gross income (MAGI) of $35,000 and earned income of $10,000, can contribute up to $7,000 to a traditional IRA or a Roth IRA. This limit is a $1,000 catch-up contribution allowed for individuals aged 50 and over, in addition to the standard limit of $6,000 for the year. Since his earned income is $10,000, Roger can contribute the full amount, as it is less than the contribution limit.