"Now, I've read that there is a mandatory 15% self-employment tax as well as additional income tax that can vary from 15-25%. Correct me if I'm wrong."---->Actually 15.3% on your gross incoem up to $106,800, I guess. It is SECA Taxes, self-employer's Soc. Sec. Tax payments, not 15%;like FICA, it is made up of your "contributions" to both the Social Security and Medicare programs.However, you can deduct 50% of the Soc. Sec. Taxes on your 1040. You, as an independent contractor, report your income on Form 1099-MISC , and the income also should be reported on line #1Schedule C or C-EZ(if applicable).If your net earnings on your Sch C is $400 or more, you must file a Schedule SE and pay SECA tax on your entire net business income( as said above), including the first $400 by filing your Sch. SE.
REMEMBER this; as nobody withholds taxes from you,( you generally will have no taxes withheld from your income). So, you may need to make quarterly estimated tax payments to both Federal and State government as you know.
"I've been putting money aside, however, I don't specifically know how much I owe. Thus far, I have made $13,481.14 and counting."---> Neither do I; due to lack of other info..i.e., expenses or etc, I can 't figure it out for you!
"I am a single college student still living with my parents. I do pay for my own tuition, if that is relevant."---> If you are a dependent of your parents, then neither your paretns nor you can deduct the educational expenses tha tyou paid on their/your tax return.
Please visit the IRS website fr further info. on SECA(estimated) Taxes; http://www.irs.gov/pub/irs-pdf/f1040es.pdf