Retirement Calculator

The retirement calculator uses two main formulas to project your financial future: one for the accumulation phase (while you're working) and one for the decumulation phase (during retirement). **Accumulation Phase Formula:** Balance(year) = Balance(year-1) × (1 + r) + C Where: - Balance(year) = Your total savings at the end of the current year - Balance(year-1) = Your total savings at the end of the previous year - r = Annual investment return rate (as a decimal, e.g., 0.07 for 7%) - C = Annual contribution amount **Decumulation Phase Formula:** Balance(year) = Balance(year-1) × (1 + r) - E(year) E(year) = E(year-1) × (1 + i) Where: - Balance(year) = Your total savings at the end of the current year - Balance(year-1) = Your total savings at the end of the previous year - r = Annual investment return rate - E(year) = Adjusted annual expenses for the current year - E(year-1) = Annual expenses from the previous year - i = Inflation rate (as a decimal, e.g., 0.03 for 3%) These formulas work together to create a comprehensive projection of your retirement savings from today through your life expectancy.

Understanding each variable is crucial to interpreting your retirement projection: **Current Age (A):** Your age today. Used to calculate the number of years until retirement. Must be between 18 and 100. This determines how many years you have to accumulate savings. **Retirement Age (R):** The age at which you plan to stop working and begin retirement. Must be greater than your current age and not exceed 100. This marks the transition from accumulation to decumulation phase. **Current Savings (S₀):** Your total retirement savings today, including 401(k), IRA, brokerage accounts, and any other retirement funds. This is your starting balance for all calculations. **Annual Contribution (C):** The amount you save each year toward retirement. This typically includes your contributions plus employer matching. Assumed to remain constant throughout the accumulation phase (though in reality, you might increase this over time). **Annual Return Rate (r):** The average annual percentage return on your investments. Historical stock market returns average 10%, but a balanced portfolio (60% stocks, 40% bonds) typically returns 7-8%. Conservative portfolios return 4-5%. This rate is applied to your balance each year. **Inflation Rate (i):** The average annual increase in prices. Historical inflation averages 3% annually. This affects your purchasing power and increases your retirement expenses each year. Your withdrawal amount increases by this rate to maintain the same lifestyle. **Life Expectancy (L):** The age to which you expect to live. Used to determine how long your retirement will last. Average life expectancy in the US is around 78-80, but you may want to use 85-90 for planning purposes to account for longevity risk. **Annual Expenses (E):** The amount you need to spend each year during retirement to maintain your desired lifestyle. This is adjusted annually for inflation. Should include housing, food, healthcare, entertainment, and all other living expenses.

Here's how the calculator processes your inputs: **Step 1: Initialize Variables** The calculator reads all eight input values and converts them to appropriate formats (percentages to decimals, etc.). **Step 2: Validate Inputs** Checks that current age < retirement age, retirement age ≤ 100, and all monetary values are non-negative. **Step 3: Accumulation Phase (Current Age to Retirement Age)** For each year from your current age to retirement age: 1. Calculate investment return: Return = Balance × r 2. Add annual contribution: Balance = Balance + C 3. Add investment return: Balance = Balance + Return 4. Store year-by-year data (age, balance, contribution, return) Example: If you're 35 with $100,000 saved, contribute $15,000 annually, and expect 7% returns: - Year 1: Balance = $100,000 × 1.07 + $15,000 = $122,000 - Year 2: Balance = $122,000 × 1.07 + $15,000 = $145,540 - And so on until retirement age 65 **Step 4: Decumulation Phase (Retirement Age to Life Expectancy)** For each year from retirement age to life expectancy: 1. Calculate investment return: Return = Balance × r 2. Adjust expenses for inflation: E = E × (1 + i) 3. Subtract adjusted expenses: Balance = Balance + Return - E 4. Ensure balance doesn't go negative (set to 0 if it does) 5. Store year-by-year data Example: If you retire at 65 with $1,000,000, need $50,000 annually, expect 7% returns, and 3% inflation: - Year 1: Expenses = $50,000, Balance = $1,000,000 × 1.07 - $50,000 = $1,020,000 - Year 2: Expenses = $50,000 × 1.03 = $51,500, Balance = $1,020,000 × 1.07 - $51,500 = $1,037,900 - And so on until life expectancy **Step 5: Generate Summary Metrics** - Balance at retirement: The balance at your retirement age - Final balance: The balance at your life expectancy - Total contributions: Annual contribution × years to retirement - Years in retirement: Life expectancy - retirement age **Step 6: Create Visualization** All year-by-year data is plotted on a line chart showing how your balance changes over time, with a clear visual transition between accumulation and decumulation phases.

The formulas used in this calculator are based on fundamental financial principles that have been proven effective for retirement planning: **Compound Interest Power:** The accumulation formula (Balance × (1 + r) + C) harnesses the power of compound interest. By multiplying your balance by (1 + r) each year, you earn returns not just on your initial savings, but also on previous years' returns. This exponential growth is why starting early is so powerful. A 25-year-old saving $5,000 annually at 7% returns will have significantly more at retirement than a 45-year-old saving the same amount. **Inflation Adjustment:** The decumulation formula adjusts expenses annually for inflation (E × (1 + i)). This is critical because $50,000 in today's dollars won't buy the same goods and services in 20 years. By increasing your withdrawal amount each year, the formula ensures you maintain your purchasing power and lifestyle throughout retirement. **Real-World Accuracy:** These formulas match how real investment accounts work. Your brokerage account calculates returns on your balance each year, and you can make withdrawals whenever you want. The calculator mirrors this real-world behavior. **Conservative Approach:** The formula assumes constant returns and contributions, which is conservative because: - Real returns vary year to year (some years up, some down) - You might increase contributions as your income grows - You might adjust spending in response to market conditions - You might receive bonuses, inheritances, or other windfalls By using average returns and constant contributions, the calculator provides a realistic baseline that accounts for market volatility. **Flexibility for Adjustments:** The formula structure allows you to easily adjust any variable to see how it affects your retirement. Want to retire 5 years earlier? Change the retirement age. Worried about market downturns? Lower the return rate. Concerned about longevity? Increase life expectancy. This flexibility makes the calculator a powerful planning tool. **Alignment with Financial Standards:** These formulas align with industry-standard retirement planning methodologies used by financial advisors, CPAs, and retirement planning software. The 4% rule, for example, is based on research showing that withdrawing 4% of your portfolio annually (adjusted for inflation) provides a high probability of not running out of money over a 30-year retirement. **Practical Validation:** You can validate the formula's accuracy by comparing results to other retirement calculators or financial planning software. The methodology is transparent and based on well-established financial principles, not proprietary black-box algorithms.