Roth IRA Calculator Formula
Understand the math behind the roth ira calculator. Each variable explained with a worked example.
Formulas Used
Projected Roth IRA Value
future_value = current_balance * pow(1 + r, years) + annual_contribution * (pow(1 + r, years) - 1) / rTotal Contributions
total_contributions = current_balance + annual_contribution * yearsTax-Free Growth
tax_free_growth = future_value - current_balance - annual_contribution * yearsVariables
| Variable | Description | Default |
|---|---|---|
current_balance | Current Roth IRA Balance(USD) | 15000 |
annual_contribution | Annual Contribution(USD) | 7000 |
annual_return | Expected Annual Return(%) | 8 |
years | Years of Growth(years) | 30 |
r | Derived value= annual_return / 100 | calculated |
How It Works
How the Roth IRA Calculator Works
A Roth IRA grows tax-free. Contributions are made with after-tax dollars, but qualified withdrawals in retirement are completely tax-free.
Formula
FV = PV × (1 + r)^n + C × [(1 + r)^n − 1] / r
The key advantage is that the growth column represents money you will never pay taxes on, unlike a traditional IRA or 401(k).
Worked Example
$15,000 balance, $7,000/yr contributions, 8% return, 30 years.
- 01Balance growth = $15,000 × (1.08)^30 = $150,940
- 02Contribution growth = $7,000 × [(1.08)^30 − 1] / 0.08 = $793,490
- 03Projected value = $150,940 + $793,490 = $944,430
- 04Total contributed = $15,000 + $7,000 × 30 = $225,000
- 05Tax-free growth = $944,430 − $225,000 = $719,430
Frequently Asked Questions
What is the Roth IRA contribution limit?
For 2026, the limit is $7,000/year ($8,000 if age 50+). Income limits apply: single filers earning above $161,000 MAGI have reduced limits.
When can I withdraw from a Roth IRA?
You can withdraw contributions anytime tax-free. Earnings can be withdrawn tax-free after age 59½ if the account has been open at least 5 years.
Roth IRA vs Traditional IRA?
Roth uses after-tax dollars with tax-free withdrawals. Traditional uses pre-tax dollars with taxed withdrawals. Choose Roth if you expect higher taxes in retirement.
Learn More
Guide
Retirement Savings Guide
A comprehensive guide to retirement savings. Learn how much you need to retire, the best account types, contribution strategies, employer matching, and how to build a retirement plan at any age.
Ready to run the numbers?
Open Roth IRA Calculator