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This calculator answers a simple but powerful question: what will a single lump sum of money grow to after earning compound interest for a given number of years? Unlike savings plans with repeated deposits, this tool models one deposit left to compound untouched. Follow the steps below.
The default example — $10,000 at 6% for 10 years — grows to $17,908.48. Notice that $7,908.48 of that total is pure interest: your money earned nearly 80% on top of itself without you lifting a finger. Try extending the term to 20 or 30 years to see compounding’s explosive late-stage acceleration — at 6%, $10,000 becomes $32,071.35 after 20 years and $57,434.91 after 30 years.
The time value of money is the foundational idea of all finance: a dollar today is worth more than a dollar tomorrow, because today’s dollar can be invested and earn interest. The present value is what money is worth right now; the future value is what it will be worth at a later date after earning interest. This calculator converts present value into future value — the most basic time-value computation there is.
Compound interest is interest calculated on both the original principal and all previously accumulated interest. Each year’s earnings join the balance and earn interest themselves the next year, creating a snowball effect. Contrast this with simple interest, which pays interest only on the original principal: $10,000 at 6% simple interest for 10 years earns a flat $600 per year, totaling $16,000 — a full $1,908.48 less than the $17,908.48 that compounding produces. Over long horizons, the gap becomes enormous: at 10% for 30 years, $1,000 grows to $4,000 with simple interest but to $17,449.40 with compound interest.
The growth factor — (1 + r)^n — is the multiplier that turns present value into future value. A growth factor of 1.7908 means every dollar becomes $1.79. Growth factors have an intuitive doubling property captured by the Rule of 72: divide 72 by the interest rate to estimate the years needed to double your money. At 6%, money doubles in about 72 ÷ 6 = 12 years; at 10%, in about 72 ÷ 10 = 7.2 years; at 3%, in about 24 years. The rule is remarkably accurate for rates between 4% and 12%.
Future value math powers nearly every financial decision: pricing bonds, valuing businesses, planning retirement, comparing investment offers, and measuring inflation’s damage. When a bank promises “6% annual growth,” when a financial advisor projects your 401(k), when an economist warns that inflation “eats” savings — all of it runs on the same formula this calculator applies. Understanding it means never again taking a growth claim at face value.
One more key distinction: nominal vs. real future value. The calculator computes nominal future value — the raw dollar figure. But if inflation averages 3% while your money earns 6%, your real (purchasing-power) growth is only about 3% per year. $10,000 compounding at 6% for 10 years gives $17,908.48 nominally, but in today’s purchasing power that is worth roughly $17,908.48 ÷ (1.03)^10 = $17,908.48 ÷ 1.343916 = $13,326.24. Always ask whether a future value is quoted in nominal or inflation-adjusted terms.
The future value of a lump sum is:
Future value = Present value × (1 + r)^n
where r is the interest rate per period (as a decimal) and n is the number of periods. The interest earned is simply future value minus present value, and the growth factor is (1 + r)^n on its own.
Worked example 1 — $10,000 at 6% for 10 years. Growth factor = (1.06)^10 = 1.7908477. Future value = $10,000 × 1.7908477 = $17,908.48. Interest earned = $17,908.48 − $10,000 = $7,908.48. The year-by-year path shows compounding’s acceleration: after 1 year the balance is $10,600.00; after 5 years it is $10,000 × (1.06)^5 = $10,000 × 1.3382256 = $13,382.26; and after 10 years it reaches $17,908.48. The second five years added $4,526.22 while the first five added only $3,382.26 — later years contribute more because the balance they compound is larger. This is the calculator’s default example.
Worked example 2 — $5,000 at 8% for 20 years. Growth factor = (1.08)^20 = 4.6609571. Future value = $5,000 × 4.6609571 = $23,304.79. Interest earned = $23,304.79 − $5,000 = $18,304.79. Here interest contributed more than triple the original deposit — $18,304.79 of growth on a $5,000 investment. Stretch the same deposit to 30 years at 8% and the growth factor becomes (1.08)^30 = 10.0626569, giving $5,000 × 10.0626569 = $50,313.28: ten times the original deposit, with $45,313.28 from compounding alone.
Reversing the formula — solving for present value. To find what you must invest today to reach a target, divide instead of multiplying: Present value = Future value ÷ (1 + r)^n. Want $100,000 in 20 years at 7%? Present value = $100,000 ÷ (1.07)^20 = $100,000 ÷ 3.869684 = $25,841.90. Invest $25,841.90 today at 7% and compounding does the remaining $74,158.10 of work.
Reversing for rate or time. To find the required rate: r = (FV ÷ PV)^(1 ÷ n) − 1. To double $10,000 to $20,000 in 10 years: r = (2)^(1 ÷ 10) − 1 = 1.071773 − 1 = 7.1773%. To find the required time: n = ln(FV ÷ PV) ÷ ln(1 + r). To triple $5,000 at 8%: n = ln(3) ÷ ln(1.08) = 1.098612 ÷ 0.076961 = 14.27 years.
The table below shows what $10,000 grows to at various rates and horizons:
| Rate | 10 years | 20 years | 30 years |
|---|---|---|---|
| 3% | $13,439.16 | $18,061.11 | $24,272.62 |
| 5% | $16,288.95 | $26,532.98 | $43,219.42 |
| 6% | $17,908.48 | $32,071.35 | $57,434.91 |
| 8% | $21,589.25 | $46,609.57 | $100,626.57 |
| 10% | $25,937.42 | $67,275.00 | $174,494.02 |
The Alvarez family has a newborn and wants $150,000 available for college in 18 years. They expect a 7% average annual return from a 529 education savings plan. How much must they deposit today as a single lump sum?
Using the reversed formula: present value = $150,000 ÷ (1.07)^18. The growth factor (1.07)^18 = 3.379932, so present value = $150,000 ÷ 3.379932 = $44,380.35. A single deposit of $44,380.35 today, compounding at 7% for 18 years, grows to exactly $150,000.
They check the journey: after 9 years (halfway through time, not halfway through growth), the balance is $44,380.35 × (1.07)^9 = $44,380.35 × 1.838459 = $81,591.55 — barely more than half the target, because compounding is back-loaded. After 14 years: $44,380.35 × (1.07)^14 = $44,380.35 × 2.578534 = $114,435.69. The final 4 years add over $35,000 — nearly a quarter of the total — demonstrating why starting early matters more than starting big: every extra year applies the growth factor to an ever-larger balance.
For comparison, waiting 5 years and then depositing means only 13 years of compounding: required deposit = $150,000 ÷ (1.07)^13 = $150,000 ÷ 2.409845 = $62,244.68 — nearly $18,000 more, the price of five years of lost compounding.
Future value math also measures what inflation destroys. Elena’s parents bought their house for $50,000 decades ago; she wonders what an equivalent house costs after 20 years of 3% annual home-price inflation. The same formula applies, with inflation as the “interest rate”: future cost = $50,000 × (1.03)^20 = $50,000 × 1.806111 = $90,305.56.
Flip the perspective: $50,000 in cash stuffed in a mattress for 20 years at 3% inflation has a present value (in today’s purchasing power) of only $50,000 ÷ 1.806111 = $27,683.85 — it lost 45% of its purchasing power doing nothing. This is why financial planners insist cash must earn at least the inflation rate: a 1% savings account during 3% inflation guarantees a ~2% annual real loss, compounded.
The exact real-return formula is (1 + nominal) ÷ (1 + inflation) − 1. At 7% nominal returns and 3% inflation: 1.07 ÷ 1.03 − 1 = 3.8835% real — slightly less than the 4% you get from simple subtraction, because the subtraction shortcut ignores compounding interaction. Over 30 years the difference matters: $10,000 at 3.8835% real grows to $10,000 × (1.038835)^30 = $10,000 × 3.1519 = $31,519 in today’s dollars, versus $32,434 with the 4% shortcut — a $915 gap from a rounding choice.
1. Using simple interest instead of compound. “6% for 10 years = 60% total” is wrong — it ignores interest-on-interest. The true growth is (1.06)^10 − 1 = 79.08%, not 60%. On $10,000 that is the difference between $16,000 (simple) and $17,908.48 (compound). The error grows with rate and time: at 10% for 30 years, simple interest gives 300% total while compounding gives (1.10)^30 − 1 = 1,644.94%.
2. Using the nominal rate when the effective rate differs. A “6%” account compounded monthly actually yields (1 + 0.06 ÷ 12)^12 − 1 = 6.1678% effective. Over 20 years, $10,000 at the true 6.1678% grows to $10,000 × (1.061678)^20 = $33,065.95 — $994.60 more than the $32,071.35 from a flat 6%. Always convert nominal quotes to effective rates before projecting.
3. Ignoring inflation. A $17,908.48 future value at 6% over 10 years sounds great until you deflate it: at 3% inflation it buys what $17,908.48 ÷ (1.03)^10 = $13,326.24 buys today. Long-range plans — retirement especially — must be built in real (inflation-adjusted) terms, or the “growth” is partly an illusion.
4. Forgetting taxes. In a taxable account, interest is taxed yearly, which cuts the compounding rate. At a 25% tax rate, a 6% return becomes 4.5% after tax: $10,000 over 20 years grows to $10,000 × (1.045)^20 = $24,117.14 instead of $32,071.35 — a $7,954.21 haircut. Tax-advantaged accounts (IRAs, 401(k)s, ISAs) exist precisely to protect the compounding engine.
5. Averaging returns arithmetically. Investment returns compound geometrically, not arithmetically. A portfolio that gains 20% then loses 20% is not flat: $10,000 × 1.20 × 0.80 = $9,600 — a 4% loss. The correct multi-year average is the geometric mean: (1.20 × 0.80)^(1 ÷ 2) − 1 = (0.96)^0.5 − 1 = −2.02% per year. Using the arithmetic average (0%) overstates long-run growth systematically.
Go further with our Future Value Calculator for more advanced projections with additional options, and our Compound Interest Calculator to see year-by-year compounding schedules with periodic contributions. You can also browse all of our Financial Calculators — more than 80 free tools covering loans, mortgages, investments, retirement planning, and everyday money math.
This page provides a future value calculator for a single lump sum with compound interest. Inputs: present value ($), annual interest rate (percent), number of years. Formula: future value = present value × (1 + r)^n; interest earned = future value − present value; growth factor = (1 + r)^n. Reference values: $10,000 at 6% for 10 years → $17,908.48 (interest $7,908.48, factor 1.7908). $5,000 at 8% for 20 years → $23,304.79. Reversals: present value = future value ÷ (1 + r)^n; required rate = (FV ÷ PV)^(1 ÷ n) − 1; required time = ln(FV ÷ PV) ÷ ln(1 + r). Rule of 72: doubling years ≈ 72 ÷ rate percent. Real return = (1 + nominal) ÷ (1 + inflation) − 1. Related resources: Future Value Calculator (https://sigmacalculator.net/financial-calculators/future-value-calculator/), Compound Interest Calculator (https://sigmacalculator.net/financial-calculators/compound-interest-calculator/), Financial Calculators index (https://sigmacalculator.net/financial-calculators/).
$17,908.48. The growth factor is (1.06)^10 = 1.7908477, so $10,000 × 1.7908477 = $17,908.48 — and $7,908.48 of that total is interest alone, not principal.
Divide your target by the growth factor: present value = future value ÷ (1 + r)^n. To have $100,000 in 20 years at 7%, deposit $100,000 ÷ (1.07)^20 = $100,000 ÷ 3.869684 = $25,841.90 today — compounding does the remaining $74,158.10 of work.
Divide 72 by the interest rate to estimate how many years it takes money to double. At 6%, money doubles in about 12 years (72 ÷ 6); at 10%, in about 7.2 years (72 ÷ 10); at 3%, in about 24 years. It is most accurate for rates between 4% and 12%.
Sources: standard time-value-of-money formulas; worked values verified against the calculator’s own outputs ($10,000 at 6% for 10 years = $17,908.48, growth factor 1.7908).