Understanding your future value result
The growth factor (1 + r)^n rises steeply with both rate and periods. These reference points illustrate the compounding effect at annual rates.
| Rate and horizon | Growth factor (1 + r)^n |
|---|---|
| 3% for 10 years | ×1.34 — money grows about a third |
| 6% for 10 years | ×1.79 — money nearly doubles |
| 6% for 24 years | ×4.05 — two doublings (Rule of 72: ~12 years each) |
| 9% for 24 years | ×7.91 — three doublings in the same time at 1.5× the rate |
- The formula assumes one compounding event per period at a constant rate, with no contributions, withdrawals, taxes or fees along the way.
- For sums compounded more often than the quoted rate's period (e.g. monthly compounding of an annual rate), divide the rate and multiply the periods accordingly — the result is slightly higher than annual compounding.
- An assumed rate is not a guaranteed return; actual investment growth varies and can be negative in any given period.
What is future value?
Future value (FV) is what a sum of money today grows to after a number of periods of compound growth at a given rate. It is one half of the time-value-of-money principle at the core of finance: money available now can earn a return, so a present amount is equivalent to a larger future amount. Standard corporate-finance texts introduce FV = PV(1 + r)^n as the first equation of the discipline.
Compounding is what distinguishes future value from simple growth. Each period, the return is earned on the original sum plus all previously accumulated growth, so value rises geometrically rather than linearly. Over long horizons this effect dominates: at 6% per year, a sum roughly doubles every 12 years (the Rule of 72 approximation: 72 ÷ 6 = 12).
The rate and the period must agree. Entering an annual rate with periods in years, or a monthly rate with periods in months, both work; mixing them does not. To convert an annual rate to monthly for this formula, divide by 12 (nominal convention) — the same convention used across loan and savings calculations.
How to use this future value calculator
- Enter the present value — the sum you have today.
- Enter the growth rate per period. Use an annual rate if your periods are years, a monthly rate if they are months.
- Enter the number of periods over which the sum compounds.
- Read the future value and the total growth (future value minus present value).
The future value formula
Future value multiplies the present value by the compound growth factor (1 + r)^n, where r is the rate per period as a decimal and n is the number of periods.
Worked example: $5,000 at 6% per year for 10 years gives FV = 5,000 × (1.06)^10 = 5,000 × 1.7908 ≈ $8,954. The growth component is about $3,954 — nearly 80% on top of the original sum, of which a substantial part is interest earned on earlier interest.
Common mistakes
- Mismatching rate and period — an annual rate with monthly periods overstates growth twelvefold in the exponent.
- Entering the rate as a whole number where a decimal is needed elsewhere; this calculator takes percent directly.
- Expecting linear growth: doubling the periods far more than doubles the growth at any positive rate.
- Ignoring inflation — the future value is nominal, and its purchasing power will be lower than today's equivalent.
- Using the Rule of 72 as exact; it is an approximation that is best near rates of 6–10%.
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How do you calculate future value?
Future value equals present value times (1 + r)^n, where r is the rate per period as a decimal and n is the number of periods. For example, $5,000 growing at 6% per year for 10 years gives 5,000 × 1.06^10 ≈ $8,954. The rate and the period length must match — annual rate with years, monthly rate with months.
What is the Rule of 72?
The Rule of 72 is a mental-math approximation for doubling time under compound growth: divide 72 by the percentage rate to get the approximate number of periods to double. At 6% per year, money doubles in about 72 ÷ 6 = 12 years; at 9%, about 8 years. The rule is most accurate for rates between roughly 6% and 10%.
What is the difference between simple and compound growth?
Simple growth earns the rate only on the original sum each period, producing linear growth: $5,000 at 6% simple gains $300 every year. Compound growth earns the rate on the accumulated balance, producing geometric growth: the same $5,000 gains $300 in year one but more each subsequent year, reaching about $8,954 after 10 years versus $8,000 under simple growth.
Can I use months instead of years as periods?
Yes. The formula is agnostic about the period length, provided the rate matches it. For monthly compounding of a 6% annual nominal rate, use r = 0.5% per month and n = 120 for ten years, giving a slightly higher result than 6% compounded annually — the difference between nominal and effective annual rates.
Does future value account for inflation?
No. The formula projects nominal dollars. To estimate purchasing power, either deflate the result by (1 + inflation)^n afterward, or use a real rate of return (approximately the nominal rate minus inflation) in the formula directly. At 2.5% inflation, $8,954 received in 10 years buys about what $6,995 buys today.
Kaynaklar
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance (13th ed.). McGraw-Hill, 2020. Chapter 2: How to Calculate Present Values.
- Bodie Z, Kane A, Marcus AJ. Investments (12th ed.). McGraw-Hill, 2021 — time value of money.
- US Securities and Exchange Commission (SEC). Investor.gov compound interest calculator. investor.gov.
- CFA Institute. Quantitative methods — the time value of money. cfainstitute.org.