To solve this problem, we need to calculate how many years it will take for the income to exceed [tex]$95,000 with an annual increase rate of 20%.
We begin with an income of $[/tex]75,000. Each year, the salary increases by 20%. Therefore, the salary for the next year will be the salary of the current year increased by 20%.
Let's calculate the salary for the first year after the current year:
Year 1:
Initial salary = [tex]$75,000
Rate of increase = 20%
We calculate the new salary by multiplying the initial salary by 1 plus the rate of increase (in decimal form).
So for year 1, the new salary would be $[/tex]75,000 * (1 + 0.20), which equals [tex]$90,000. This new salary is still below the $[/tex]95,000 limit, so you would still be eligible to contribute to a ROTH IRA.
Now, let's calculate the salary for the second year after the current year:
Year 2:
Previous year's salary = [tex]$90,000
Applying the same formula, the new salary would be $[/tex]90,000 * (1 + 0.20), which equals [tex]$108,000. This salary exceeds the $[/tex]95,000 limit, meaning that after this point, you would no longer qualify to set up a ROTH IRA.
However, the question asks how many "more years" after the current year can you contribute. After the first year post-current year, your salary is still below [tex]$95,000. It's not until the second year after the current year that your salary exceeds the limit.
Therefore, it is in that second year (the first year being under $[/tex]95,000) that you would no longer be eligible. Hence, you have only one more year after the current year to contribute to a ROTH IRA before you are disqualified due to the income exceeding the limit.
So the correct answer is:
a) 1 year
