No, you will not need to combine the two totals to figure out the contribution limit. While they are both retirement plans, your 403(b) annuity is not an IRA. The IRS does not restrict how much you contribute to a Roth IRA based on whether or not you qualify for and contribute to another type of retirement plan (such as a pension plan that is not an IRA), but it does restrict you based on your overall income. For more information, please see the following IRS website: https://www.irs.gov/retirement-plans/plan-participant-employee/amount-of-roth-ira-contributions-that...
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