Roth IRA Calculator Formula

Understand the math behind the roth ira calculator. Each variable explained with a worked example.

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Formulas Used

Projected Roth IRA Value

future_value = current_balance * pow(1 + r, years) + annual_contribution * (pow(1 + r, years) - 1) / r

Total Contributions

total_contributions = current_balance + annual_contribution * years

Tax-Free Growth

tax_free_growth = future_value - current_balance - annual_contribution * years

Variables

VariableDescriptionDefault
current_balanceCurrent Roth IRA Balance(USD)15000
annual_contributionAnnual Contribution(USD)7000
annual_returnExpected Annual Return(%)8
yearsYears of Growth(years)30
rDerived value= annual_return / 100calculated

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.

current_balance = 15000annual_contribution = 7000annual_return = 8years = 30
  1. 01Balance growth = $15,000 × (1.08)^30 = $150,940
  2. 02Contribution growth = $7,000 × [(1.08)^30 − 1] / 0.08 = $793,490
  3. 03Projected value = $150,940 + $793,490 = $944,430
  4. 04Total contributed = $15,000 + $7,000 × 30 = $225,000
  5. 05Tax-free growth = $944,430 − $225,000 = $719,430

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