Compound Interest Tool

Enter a starting balance, monthly deposit, time horizon, and assumed rate to calculate a savings scenario. The result separates contributions from growth and shows each year-end balance. Compare several rates and deposit amounts to see which assumptions drive the outcome.

Contributions enter at the end of every month. The frequency selector converts a nominal annual rate into an effective annual rate, then into an equivalent monthly growth rate. This keeps deposit timing consistent across comparisons. For quarterly and annual settings, that conversion is a fractional-period modeling convention; a bank may instead calculate and credit actual interest using its own daily-balance rules.

How to enter the five inputs

Enter the money already set aside as initial principal. Enter only new monthly deposits in the contribution box; do not divide the existing balance by the number of months and enter it again. For the time horizon, use a whole number of years between 0 and 60. A zero-year scenario returns the starting balance.

Enter a nominal annual rate before the selected compounding adjustment. Accepted inputs are 0%–25%, principal up to $1 billion, and monthly deposits up to $10 million. Blank, negative, nonfinite, or out-of-range values produce an error. Choose the rate from the scenario you want to examine and use a lower-rate comparison as well.

If you have an effective annual return or a bank’s advertised APY, choose the annual setting and enter that percentage to avoid compounding it twice. In this simplified model, a 4.5% APY applied to $10,000 for one year with no deposits produces $450 of growth. Selecting daily or monthly compounding again would incorrectly treat that APY as a nominal rate.

What the calculation does

Let r be the nominal annual rate expressed as a decimal, and f the selected compounding frequency: 1, 4 or 12. The effective annual rate is (1 + r/f)^f − 1. The equivalent monthly growth rate is j = (1 + r/f)^(f/12) − 1.

Each month, the calculator multiplies the current balance by 1+j, then adds the contribution. Deposits therefore receive no growth in the month they enter. After 12 months it records the balance, cumulative contributions and difference between them. It retains full numerical precision during the projection and rounds currency only for display.

For N = 12 × years, starting principal P and monthly deposit M, the independent closed-form check is:

final balance = P × (1+j)^N + M × ((1+j)^N − 1) / j

At zero growth, the formula becomes P + M × N. The result’s modeled growth equals the final balance minus starting principal and deposits. At a zero rate, all of the ending balance therefore comes from money contributed.

Worked example using the default inputs

With $10,000 initially, $500 deposited at each month-end, a hypothetical 7% nominal annual rate, monthly compounding and 30 years, the monthly rate is 0.07/12 and there are 360 deposits.

Component	Calculated value
Future value of the initial $10,000	$81,164.97
Future value of the monthly deposits	$609,985.50
Final balance	$691,150.47
Principal plus deposits	$190,000.00
Modeled growth	$501,150.47

Contributions total $10,000 + $500 × 360 = $190,000. Monthly compounding raises the effective annual rate from the nominal 7% to about 7.229%. The example holds that rate constant and excludes taxes, fees, and withdrawals.

Try the same inputs at 0%. The final balance becomes $190,000 and modeled growth becomes zero. This provides a useful check that the deposits are entered correctly before experimenting with other rates.

Compare compounding without moving the deposits

Holding the nominal rate at 7% gives different effective annual rates. Here is the same 30-year scenario, with the $500 deposit still made every month under each setting:

Nominal-rate compounding	Effective annual rate	Final balance
Annual	7.000%	$660,848.85
Quarterly	7.186%	$685,332.19
Monthly	7.229%	$691,150.47

This comparison uses equivalent monthly growth for the annual and quarterly settings. It does not postpone deposits until year-end or quarter-end. If you actually make one $6,000 deposit each year instead of $500 monthly, that is a different cash-flow pattern and requires a different calculation.

Without any new deposits, $10,000 becomes $76,122.55, $80,191.83 or $81,164.97 under annual, quarterly or monthly compounding respectively. This isolates the frequency effect from contribution timing. If you instead hold the effective annual rate constant, the frequency label alone does not create additional annual earnings.

Use APY and rate disclosures correctly

The CFPB’s APY rules define annual percentage yield using both the interest rate and compounding. When comparing deposit accounts, use the disclosed APY and read conditions such as variable rates, balance tiers and fees. A headline rate that applies only to part of a balance should not be applied to the entire account.

The CFPB’s compound-interest explanation describes interest accumulating on previously earned interest. With an investment portfolio, reinvested returns can also compound mathematically, but stock prices and distributions do not behave like a fixed contractual interest rate. “Growth” is the appropriate interpretation for an investment scenario.

For a lump-sum scenario, $50,000 at 8% nominal interest compounded quarterly for 25 years becomes about $362,232.31: 50000 × 1.02^100. Each modeled quarter earns 2%. Enter zero monthly contributions to isolate this effect in the calculator.

Account for inflation and fees outside the tool

The output is nominal future dollars. If inflation averages 3% for 30 years, a future $1 million has approximately $411,987 of starting-year purchasing power, calculated as 1000000 / 1.03^30. You cannot compare an unadjusted future balance directly with today’s spending needs.

For a hypothetical 7% effective annual return and 3% inflation, the exact real return is 1.07 / 1.03 − 1, about 3.883%. Subtracting inflation gives an approximation, not the exact compounded relationship. If using a real return, select annual conversion and keep all spending targets and contributions in a compatible purchasing-power convention.

Fees also reduce results. You can enter a simplified after-fee return assumption, but avoid subtracting expenses again from a fund return that already reflects them. Actual advisory billing, taxes, realized gains and changing balances require more detailed modeling than one constant percentage.

Understand volatility and the Rule of 72

The Rule of 72 approximates doubling time by dividing 72 by the percentage return. At 7%, the estimate is 10.29 years, compared with 10.24 years from ln(2)/ln(1.07) for a constant 7% effective annual return and no deposits. Use the exact formula when the difference matters to the calculation.

Arithmetic average returns can mislead. A hypothetical 20% gain followed by a 20% loss leaves $10,000 at $9,600, despite an arithmetic average of zero. With no intervening cash flows, reversing those two returns gives the same final result. With contributions or withdrawals, their order can affect the outcome because different amounts are exposed in each period.

Save a base scenario, a lower-return scenario, and a smaller-deposit scenario. Compare the contribution total and final balance in each. If saving pauses for part of the period, model the segments separately so that the cash-flow change is visible.

Sources

• SEC Investor.gov: Compound Interest Calculator
• CFPB: How compound interest works
• CFPB: APY calculation rules

Source pages checked November 3, 2026. The tool uses the constant-rate, month-end-deposit model described above.