To calculate future value, multiply your starting amount by one plus the interest rate, raised to the number of periods: FV = PV × (1 + r)^n. That single formula handles a lump sum earning compound interest. If your rate compounds more than once a year, or if you’re adding money regularly instead of investing once, the formula shifts slightly but the idea is the same. Money earns a return, that return earns its own return, and time does most of the work.
The rest of this article walks through each version of the calculation with worked numbers, then shows how to adjust the result for compounding frequency, inflation, and taxes so the answer reflects what your money will actually be worth.
The Three Inputs You Need
Every future value calculation uses a starting amount, an interest rate, and a time period. Small errors in any of them compound into large errors over long horizons, so it pays to pin each one down before running the math.
The present value (PV) is your starting balance. For a certificate of deposit, it’s the figure on your account statement. For an investment, it’s the current market value or the initial deposit. If you’ve already earned interest in prior years, a Form 1099-INT from your bank confirms those earnings and helps you set the correct starting figure for the next period.1Internal Revenue Service. About Form 1099-INT
The interest rate (r) must be in decimal form. Divide the percentage by 100 before plugging it in, so 5% becomes 0.05. Watch the difference between APR and APY on your account paperwork: APR is the stated rate before compounding, while APY reflects compounding and shows what you actually earn in a year. For the future value formulas below, use the nominal annual rate (the APR-equivalent figure) and let the formula’s compounding term handle the rest. Otherwise you’ll double-count compounding.
Federal law makes these numbers easy to find. The Truth in Lending Act requires lenders to disclose APR on credit products, and the Truth in Savings Act, implemented through Regulation DD, requires banks to disclose both the interest rate and the APY on deposit accounts.2Federal Deposit Insurance Corporation. Truth in Lending Act (TILA)3eCFR. 12 CFR Part 1030 – Truth in Savings (Regulation DD) The figures appear on your account agreement, loan disclosure, or brokerage statement.
The time period (t) is how many years your money stays invested. Loan contracts and CD agreements specify this directly. For an open-ended savings account, choose the horizon that fits your planning: five years, ten years, thirty years to retirement.
Simple Interest Future Value
Simple interest accrues only on the original principal, never on interest already earned. The formula is:
FV = PV × (1 + r × t)
Deposit $10,000 at 4% simple interest for 10 years and the math is straightforward: FV = $10,000 × (1 + 0.04 × 10) = $10,000 × 1.40 = $14,000. You earn exactly $400 a year, every year, regardless of what’s already accumulated.
You’ll see simple interest on certain short-term personal loans, some Treasury instruments, and legal judgments where a court awards prejudgment interest that doesn’t compound. It’s uncommon in everyday savings, but knowing it gives you a baseline.
Compound Interest Future Value
Compound interest adds each period’s earnings back to the balance, so the next period’s interest is calculated on a larger amount. This is the formula that governs most savings accounts, CDs, and investment accounts:
FV = PV × (1 + r/n)^(n × t)
- FV: future value
- PV: present value
- r: annual interest rate as a decimal
- n: compounding periods per year
- t: time in years
Take the same $10,000 at 4% for 10 years, but compound monthly (n = 12): FV = $10,000 × (1 + 0.04/12)^(12 × 10) = $10,000 × (1.00333)^120 ≈ $14,908. That’s $908 more than simple interest produced, and the gap widens sharply with longer time horizons or higher rates. Leave the same account alone for 20 years and it reaches roughly $22,167, more than doubling without a single additional deposit.
The exponent does the heavy lifting. Raising a number slightly greater than one to a large power is what creates geometric growth.
How Compounding Frequency Changes the Answer
The “n” in the compound interest formula matters more than most people expect. Interest that compounds monthly grows faster than interest compounded annually at the same stated rate, because each month’s interest starts earning its own return sooner.
Here’s $10,000 at 4% for 10 years under different compounding schedules:
- Annually (n = 1): $14,802
- Quarterly (n = 4): $14,889
- Monthly (n = 12): $14,908
- Daily (n = 365): $14,918
The differences look small at 4% over 10 years, but they scale up with higher rates and longer periods. Regulation DD exists precisely because these distinctions matter to consumers; it requires banks to disclose how often interest compounds and to express the effective rate as an APY so you can compare accounts on equal footing.3eCFR. 12 CFR Part 1030 – Truth in Savings (Regulation DD)
The Rule of 72 for Quick Estimates
When you don’t need precision, the Rule of 72 gives you a fast mental estimate of doubling time. Divide 72 by the annual interest rate and the result is roughly the number of years for your money to double.4Investor.gov. What Is Compound Interest?
At 6%, your money doubles in about 12 years. At 4%, roughly 18 years. At 9%, about 8. The rule works best for rates between 2% and 12%. Reverse it too: if someone claims an investment will double in five years, the implied return is around 14.4%, which should prompt some questions about the risk.
Future Value of Regular Contributions
Most people don’t invest a lump sum and walk away. They contribute regularly, whether that’s monthly retirement deposits, annual IRA contributions, or periodic payments into a college fund. Calculating the future value of repeated equal payments requires an annuity formula.
Ordinary Annuity: Payments at the End of Each Period
An ordinary annuity assumes each payment lands at the end of the period, like a paycheck deduction hitting your 401(k) on the last day of the month. The formula is:
FV = PMT × [((1 + i)^n − 1) / i]
- PMT: payment amount per period
- i: interest rate per period (annual rate ÷ periods per year)
- n: total number of payments
Invest $200 a month for 20 years at a 6% annual return (i = 0.005 per month, n = 240 payments): FV = $200 × [((1.005)^240 − 1) / 0.005] ≈ $92,408. Your out-of-pocket contributions over that period total $48,000, so compound growth nearly doubled what you put in.
Annuity Due: Payments at the Start of Each Period
When payments land at the beginning of each period rather than the end, each one gets an extra period of growth. Calculate the ordinary annuity value first, then multiply by (1 + i):
FV (annuity due) = PMT × [((1 + i)^n − 1) / i] × (1 + i)
With the same $200 a month at 6% for 20 years: $92,408 × 1.005 ≈ $92,870. The difference of about $462 is modest here but widens with larger payments, higher rates, or longer time frames.
Adjusting for Inflation
A future value calculation tells you the nominal number of dollars you’ll have. It says nothing about what those dollars will buy. A million dollars in 30 years won’t cover what a million dollars covers today.
The Federal Reserve targets a long-run inflation rate of 2.0% for the U.S. economy.5Federal Reserve. FOMC Projections Materials, March 18, 2026 To convert a nominal future value into real, inflation-adjusted terms, first calculate the real rate of return:
Real return = [(1 + nominal return) / (1 + inflation rate)] − 1
An investment earning 6% nominally with 2% inflation has a real return of [(1.06) / (1.02)] − 1, or roughly 3.9%. Run the future value formula using 3.9% instead of 6% and the result expresses the future balance in today’s purchasing power. For retirement planning, this is the more honest number.
Adjusting for Taxes
Taxes quietly chip away at investment growth. Interest earned on savings accounts, CDs, and most bonds counts as ordinary income and is taxed in the year you earn it. Financial institutions report interest of $10 or more on Form 1099-INT, but you owe tax on all interest regardless of whether a 1099 arrives.6Internal Revenue Service. Topic No. 403, Interest Received
To build taxes into the projection, reduce the interest rate by your marginal tax rate before running the formula:
After-tax rate = pre-tax rate × (1 − tax rate)
A 4% savings account for someone in a 24% marginal federal bracket has an effective rate of 4% × 0.76 = 3.04%. Over 10 years with monthly compounding, $10,000 grows to roughly $13,540 after tax, compared with $14,908 if you ignored taxes. The $1,368 gap is real money, and it grows at higher rates and longer horizons.
Tax-advantaged accounts change this picture. Traditional 401(k)s and IRAs compound tax-deferred, so you don’t pay tax annually on the gains, but withdrawals in retirement are taxed as ordinary income. A Roth IRA flips it: contributions go in after-tax, but qualified withdrawals come out tax-free. For projections in these accounts, use the pre-tax rate during accumulation, then apply taxes at withdrawal (traditional) or not at all (Roth).
What the Formula Can’t Tell You
Future value formulas are precise, but precision isn’t the same as accuracy. Every version above assumes a constant rate of return for the entire horizon. Real returns bounce around. Markets crash, interest rates shift, and bonds default. The formula produces a single clean number, but actual outcomes fall within a range around it, and the range widens the further out you project.
For fixed-rate instruments like CDs, the formula is reliable because the rate is contractually locked in. For variable-rate savings accounts or equity investments, treat the answer as a planning estimate. It tells you what happens if your assumptions hold, which is useful for setting savings targets and comparing scenarios. It is not a guarantee.
The biggest practical mistake is ignoring taxes and inflation together. A nominal projection of $500,000 in a taxable account over 30 years might represent only $280,000 in today’s purchasing power once both drags are counted. Running the formula three ways, nominal then inflation-adjusted then after-tax-and-inflation-adjusted, gives you a much clearer picture. The SEC also offers a free compound interest calculator at investor.gov if you’d rather skip the arithmetic.7Investor.gov. Compound Interest Calculator