Compound Interest Calculator
Calculate how your investments grow with compound interest. See the power of compounding with monthly contributions.
Reviewed by the Calcura editorial team · Last reviewed
- Question
- How do I calculate compound interest with monthly contributions?
- Answer
- Future value equals the principal compounded plus the accumulated value of all contributions: FV = P(1 + r/n)^(n·t) + PMT × [((1+r/n)^(n·t) − 1) / (r/n)], where P is the starting balance, PMT is the regular contribution per period, r is the annual rate (decimal), n is compounding periods per year, and t is time in years. Example: $10,000 at 7% compounded monthly with $500 added per month for 20 years grows to about $299,400.
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- Formula
FV = P(1 + r/n)^(n·t) + PMT × [((1+r/n)^(n·t) − 1) / (r/n)]- Caveats
- Assumes a fixed rate. Real returns vary year to year.
- Does not account for taxes on interest or capital gains.
- Inflation reduces the purchasing power of the future value — subtract ~2-3%/year for a real-terms estimate.
What This Calculator Does
This calculator projects how a balance grows when interest is earned on both the original principal and on interest already accumulated. It supports a starting balance, regular monthly contributions, a fixed annual rate, and a time horizon, and it returns the future value using the standard compound-interest-with-annuity formula. Use it to see how far a savings or investment plan could go under a given set of assumptions — not to guarantee a specific outcome.
When To Use This Calculator
Projecting long-term retirement savings
You have $15,000 in a retirement account, can add $500/month, and want to see what 35 years at a 7% assumed annual return looks like. The calculator turns those four inputs into a single projected balance you can compare against your retirement goal.
Comparing a savings account against an investment account
Run the same principal and monthly contribution twice — once at a savings-account rate (e.g. a 4–5% APY quoted today) and once at a higher assumed investment return — to see the dollar gap the rate difference creates over your chosen horizon.
Seeing the cost of starting later
Run the calculator twice with the same monthly contribution and rate but different horizons (30 years vs. 20 years). The difference shows the dollar cost of waiting ten years to start — compounding rewards time more than it rewards contribution size.
Reverse-engineering a savings target
You need a specific amount by a specific date (down payment, tuition, sabbatical). Try different monthly contributions at a conservative rate until the projected future value matches your target.
How It Works
Compound interest earns a return on the principal and on returns already credited. When a contribution is added each period, that contribution also starts earning from the moment it lands. This calculator compounds monthly: the annual rate is divided by 12, and each month the balance is multiplied by (1 + monthly rate) before the next contribution is added. Real-world returns are not smooth — markets rise and fall, and the final balance in any given year can differ from the projection even if the long-run average matches. Treat the output as a planning estimate, not a guaranteed outcome.
Formula
FV = P(1+r)^n + PMT × [((1+r)^n − 1) / r], where P = principal, r = periodic rate (annual ÷ 12), n = total periods (years × 12), PMT = contribution per period.Real-World Example
Scenario
A saver starts with $5,000, adds $400 each month, and earns a constant 7% annual return compounded monthly. How large is the balance after 30 years?
Calculation
r = 0.07 / 12 ≈ 0.005833 n = 30 × 12 = 360 FV = 5,000 × (1.005833)^360 + 400 × [((1.005833)^360 − 1) / 0.005833] FV ≈ 5,000 × 8.1165 + 400 × 1,219.97 FV ≈ 40,582 + 487,988
Result
Approximately $528,570. Total contributed: $5,000 + (360 × $400) = $149,000. Everything above that — roughly $379,000 — is compounded growth under the 7% assumption.
Common Mistakes to Avoid
Mistake: Assuming a high, smooth rate of return
Solution: Historical long-run U.S. stock returns have averaged around 10% nominal, but individual years vary widely and inflation erodes purchasing power. For planning, a 5–7% real-return assumption is more defensible than 10% nominal.
Mistake: Ignoring fees and taxes
Solution: A 1% annual expense ratio or advisory fee compounds against you the same way returns compound for you. In a taxable account, dividends and realized gains are taxed yearly. Run the projection at net-of-fee, net-of-tax rates for a realistic picture.
Mistake: Treating the projection as a guarantee
Solution: Compound-interest math assumes a fixed rate. Real markets don't deliver that. Use the calculator to compare scenarios (starting sooner, contributing more, different rates), not to promise yourself a specific number.
Mistake: Forgetting about inflation
Solution: A balance of $500,000 in 30 years is worth less than $500,000 today. Either use a real (inflation-adjusted) rate of return, or mentally discount the result by expected inflation to compare it against today's purchasing power.
Compound Interest vs. Related Calculators
Simple Interest Calculator
Interest earned only on the original principal, with no compounding. Useful for short-term loans, some bonds, and any product that explicitly quotes simple interest.
Retirement Calculator
Adds retirement-specific assumptions — contribution limits, target withdrawal rate, retirement age — on top of compound growth. Use after you understand how compounding itself behaves.
Savings Growth Calculator
Similar math, framed around a savings goal rather than an investment horizon. Useful for short-to-medium-term goals at savings-account rates.
When This Isn't the Right Tool
Variable-rate or market-linked accounts
Use instead: If the rate changes with market conditions (most investment accounts, variable-rate bonds), a single-rate projection will overstate certainty. Run best-case and worst-case rates to bracket the outcome.
Debt payoff (credit cards, loans)
Use instead: For amortizing debt, use a dedicated loan or credit-card payoff calculator — the cash flows go the opposite direction and the math incorporates minimum payments and payoff order.
Tax-specific planning decisions
Use instead: This calculator is pre-tax. For choices that depend on after-tax outcomes (Roth vs. Traditional IRA, taxable vs. tax-deferred accounts), consult IRS guidance or a qualified tax professional.
How to Verify This Calculation
To sanity-check the result, drop your inputs into a spreadsheet: =FV(rate/12, years*12, -pmt, -principal). Google Sheets and Excel both implement the same compound-interest-with-annuity formula. If the numbers disagree by more than a rounding cent, one of the inputs (rate as decimal vs. percent, monthly vs. annual period) is off.
Sources
- U.S. Securities and Exchange Commission — Compound Interest Calculator (Investor.gov) — Official SEC calculator useful for cross-checking outputs.
- Consumer Financial Protection Bureau — How does compound interest work? — Plain-language explanation of compounding for consumers.
- U.S. Treasury — Savings Bond and interest basics — Primary source for U.S. savings products and their compounding conventions.
Reviewed by the Calcura editorial team · Last reviewed