Project investment growth with compound interest, regular contributions, multiple compound frequencies, and inflation adjustment.
Computes future value using A = P(1+r/n)^(nt) plus the periodic contribution annuity adjustment, with toggles for daily, monthly, quarterly, or annual compounding and begin/end-of-period contribution timing. Outputs nominal balance, total contributions, interest earned, today's dollars after inflation, and a year-by-year breakdown.
Disclaimer: Past returns do not guarantee future performance. Inflation and tax treatment in tax-advantaged accounts (401k, IRA, HSA in the US) materially affect real returns.
Calculator information
📋 How to use this calculator
- Enter the initial principal (your first investment amount). Example: $5,000 or $50,000.
- Enter the annual interest rate / APR. Example: 7% for historical S&P 500 average, 4.5% for a high-yield savings account.
- Choose compounding frequency: daily, monthly, quarterly, semi-annually, or annually. Most US high-yield savings accounts compound daily.
- Set the investment horizon in years (1-50) and your periodic contribution (e.g., $500/month for dollar-cost averaging).
- Pick contribution timing: beginning-of-period (annuity due) or end-of-period (ordinary annuity); end-of-period is more common.
- Enable inflation adjustment using a long-run assumption (Federal Reserve targets 2%; use 2.5-3% for conservative planning) to view results in today's dollars.
- Tip: For an apples-to-apples comparison between products, look at APY (effective annual yield), not just APR.
🧮 Compound Interest with Periodic Contributions
A = P*(1 + r/n)^(n*t) + PMT * [((1 + r/n)^(n*t) - 1) / (r/n)] * (1 + r/n)^k
- A = future value
- P = initial principal
- r = annual interest rate (decimal, e.g., 0.07)
- n = number of compounding periods per year (12 for monthly, 365 for daily)
- t = term in years
- PMT = contribution per period (matching n)
- k = 1 for beginning-of-period (annuity due), 0 for end-of-period (ordinary annuity)
APY = (1 + r/n)^n - 1. Inflation adjustment: real_value = nominal / (1 + inflation)^t. US tax treatment: interest from savings accounts and CDs is taxed as ordinary income; long-term capital gains on stocks held over 1 year are taxed at 0%, 15%, or 20% depending on income bracket. Tax-advantaged accounts (401(k), IRA, Roth IRA, HSA) defer or eliminate these taxes.
💡 Worked example: Initial $10,000 plus $1,000/month DCA, 10 years at 8% return
Given:- Principal P: $10,000
- APR r: 8% (0.08)
- Compounding n: monthly (12)
- Term t: 10 years
- PMT: $1,000 per month, end-of-period
Steps:- r/n = 0.08 / 12 = 0.006667.
- n*t = 120.
- Principal growth factor: (1.006667)^120 = 2.2196.
- Future value of principal: 10,000 * 2.2196 = $22,196.
- Annuity factor: (2.2196 - 1) / 0.006667 = 182.946.
- Future value of contributions: 1,000 * 182.946 = $182,946.
- Total A = 22,196 + 182,946 = $205,142.
- Total contributed: 10,000 + (1,000 * 120) = $130,000.
- Interest earned: 205,142 - 130,000 = $75,142.
Result: After 10 years, $205,142 accumulated; $75,142 in interest. At 3% annual inflation, purchasing power equals roughly $152,600 in today's dollars.
❓ Frequently asked questions
What's the difference between APR and APY?
APR (Annual Percentage Rate) is the nominal annual interest rate without accounting for compounding. APY (Annual Percentage Yield) or effective rate includes the effect of compounding and is therefore higher. Example: a 12% APR with monthly compounding equals a 12.68% APY. The federal Truth in Savings Act requires US banks to disclose APY on deposit accounts so consumers can compare them fairly.
Why is the real return smaller than the nominal return?
Inflation erodes purchasing power over time. If inflation averages 3% per year over 10 years, $100,000 today equals about $74,400 in purchasing power. The Federal Reserve targets 2% long-run inflation; use 2.5-3% for conservative planning, especially given periods of elevated inflation like 2021-2023.
Does the calculator automatically account for taxes?
Standard calculators don't deduct taxes. For after-tax results in the US: interest from savings accounts, CDs, and bonds is taxed as ordinary income (10-37% federal plus state); qualified dividends and long-term capital gains face 0%, 15%, or 20% federal rates. Tax-advantaged accounts - 401(k), Traditional IRA (tax-deferred), Roth IRA / Roth 401(k) (tax-free withdrawals), and HSA (triple tax advantage) - dramatically improve net returns.
Why isn't daily compounding much better than monthly?
Compounding frequency has diminishing returns. At 6% APR: monthly APY is 6.17%, daily APY is 6.18%, continuous APY is 6.184%. The difference between monthly and daily is only 0.01%, which is negligible for short horizons. Focus instead on APR and the size of your periodic contribution.
Beginning-of-period vs end-of-period contributions - which is better?
Beginning-of-period (annuity due) yields slightly more because each contribution gets one extra period to compound. For $1,000 monthly DCA over 30 years at 8%, the difference is about 0.7% on the final balance. In practice, if you automate contributions on payday (typically the 1st or 15th), use beginning-of-period to model the early-month deposit.
📚 Sources & references
Last updated: May 11, 2026