Compound Interest Calculator
Inputs
| Strategy | Accumulation — saving / contributing |
|---|---|
| Compounding Frequency | Monthly |
| Starting Principal | 10,000 $ |
| Monthly Cashflow | 500 $ |
| Annual Interest Rate | 6 % |
| Investment Duration | 20 yr |
| Annual Inflation Rate | 0 % |
Visualization
Compound Interest Calculator
Calculate compound interest on a principal with optional monthly contributions or withdrawals, inflation adjustment, and side-by-side scenario comparison.
Inputs
Starting Point & Cashflow
Rate & Horizon
Inflation Adjustment (optional)
Results
Enter a value to see results.
Details
Scenarios
Save the current inputs as a scenario to compare side-by-side.
Compound interest
Compound interest is the method of crediting interest on both the original principal and on all previously accumulated interest, so each period's interest itself earns interest in subsequent periods. The balance therefore grows geometrically rather than linearly. Simple interest on $10,000 at 6% produces $600 per year every year; compound interest produces $600 in year 1, roughly $636 in year 2 (because year 1's $600 has now also started earning), and so on — the gap widens every year.
This calculator covers two modes. Accumulation models building a balance over time through an initial deposit and optional regular contributions. Decumulation models drawing a portfolio down with regular withdrawals — the underlying math is the same formula with the cashflow sign reversed.
Formula
The future balance after years combines the compounded principal with the future value of a stream of monthly cashflows :
FV=P(1+nr)nt+C⋅(1+nr)n/12−1(1+nr)nt−1where is the starting principal, is the annual interest rate (as a decimal), is the compounding frequency in periods per year, is time in years, and is the monthly cashflow (positive for contributions, negative for withdrawals). The denominator factor converts between a monthly contribution rhythm and whatever compounding cadence is selected. When $n = 12$ the formula reduces to the standard textbook monthly form; when $r = 0$ it collapses to the linear $P + 12Ct$.
The real (inflation-adjusted) balance applies a deflator to the nominal result:
FVreal=(1+i)tFVwhere is the annual inflation rate.
Worked example
Inputs: starting principal $P = $10{,}000$, monthly contribution $C = $300$, annual rate $r = 6%$ (0.06), monthly compounding $n = 12$, time $t = 20$ years.
Step 1 — compute the growth factor :
g=(1+120.06)12×20=(1.005)240≈3.3102Step 2 — principal term:
P⋅g=10,000×3.3102=$33,102Step 3 — monthly-contribution denominator:
q=(1.005)12/12−1=1.005−1=0.005Step 4 — annuity term:
C⋅qg−1=300×0.0053.3102−1=300×0.0052.3102=300×462.04=$138,612Step 5 — final balance:
FV=33,102+138,612=$171,714Total contributions over 20 years: = $82{,}000. Interest earned: $171{,}714 - 82{,}000 = $89{,}714$ — more than the money contributed.
Compounding frequency has a real but diminishing effect. For a single $10,000 deposit at 6% over 30 years (no monthly contribution), the outcome by frequency is:
| Compounding | Final balance |
|---|---|
| Annual | $57,435 |
| Quarterly | $59,693 |
| Monthly | $60,226 |
| Daily | $60,484 |
The gap between annual and monthly is meaningful; the gap between monthly and daily is negligible. The choice of investment vehicle turns on fees, asset class, and tax treatment — not on marginal compounding cadence.
A useful order-of-magnitude heuristic is the rule of 72: dividing 72 by the annual interest rate gives the approximate number of years for the principal alone to double. At 6% that is roughly 12 years; at 9%, roughly 8 years. The rule understates the contribution of regular cashflows but gives an immediate intuition for why small differences in rate matter greatly over long horizons.
Decumulation and the 4% rule
In decumulation mode the monthly cashflow is subtracted from the balance each period. The classic retirement-planning question is: how long does a portfolio sustain a given withdrawal rate? The 4% rule comes from the Trinity Study — a 1998 paper by three Trinity University finance professors that analyzed how long retirement portfolios survived at various withdrawal rates across historical market returns — which found that withdrawing 4% of starting principal per year, adjusted for inflation, preserved a stock-heavy portfolio through 30-year horizons in roughly 95% of historical periods.
Two limitations the constant-rate model cannot capture:
- Sequence-of-returns risk. A severe early bear market permanently impairs a withdrawing portfolio in a way the same average return experienced in the opposite order would not. A constant-rate calculator smooths over this risk entirely.
- Inflation-adjusted withdrawals. The 4%-rule literature adjusts the annual withdrawal for consumer-price inflation (CPI) each year. To approximate this, set the monthly withdrawal to roughly 4% of starting principal divided by 12 and enable the inflation overlay to track real purchasing power.
Comparing strategies side by side
The scenarios view locks in a set of inputs as a baseline snapshot, so one variable can be adjusted at a time against it. Useful comparisons:
- Time vs. contribution amount. Snapshot $500/month for 30 years against $1,000/month for 20 years. Total contributions are similar; the final balances are not — time is the dominant variable.
- Rate sensitivity. Shift the rate from 5% to 7% and observe how differently the curves diverge over the last decade of a long horizon.
- Inflation drag. Compare the nominal and real curves at 2% and 4% inflation to see how fast purchasing power erodes in long-horizon plans.
For goal-oriented savings planning — working backward from a target amount to the required monthly contribution — see Savings Goal & Growth Calculator. To measure how inflation erodes a specific balance in real terms over time, see Inflation Calculator.
Frequently Asked Questions (FAQ)
How does compounding frequency actually matter?
Higher frequencies credit interest more often, which slightly accelerates growth. At 6% annual rate over 30 years on $10,000: annual compounding yields ~$57.4k, monthly ~$60.2k, daily ~$60.5k. The gap between monthly and daily is tiny; the gap between annual and monthly is meaningful but not dramatic.
What is the difference between this and the savings calculator?
The savings calculator focuses on goal-seeking ("how much do I need to save?") with monthly compounding hardcoded. This calculator is general-purpose — frequency-aware, supports decumulation, and has a scenarios parallel-view for comparing strategies side-by-side.
How reliable is the 4% rule as a withdrawal guideline?
The 4% rule is a heuristic, not a guarantee. The Trinity Study — a 1998 paper by three Trinity University finance professors that analyzed retirement portfolio survival rates — found that a 4% inflation-adjusted withdrawal rate from a stock-heavy portfolio survived 30-year horizons in approximately 95% of historical periods.
Sequence-of-returns risk, longer planning horizons, and lower-yield environments can each undermine it. This calculator can stress-test a specific set of numbers against the heuristic.
Why is total interest sometimes higher than my contributions?
Compound interest. Each year's interest earns interest the next year. Over 30+ years at typical equity returns, the final balance is often 3–5× the total contributions. The crossover point — where cumulative interest exceeds cumulative contributions — is where compounding contributes most of the growth.
Disclaimer
This calculator assumes constant monthly cashflows, a constant nominal rate of return, and constant inflation. Real markets are volatile: taxes and fees reduce returns, sequence-of-returns risk matters in decumulation, and inflation varies year to year.
Results are estimates for planning purposes only, not financial advice. Consult a qualified financial adviser for individualized retirement or large-balance guidance.