Future Value Calculator

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Reviewed by: Dr. Elias Vance, Ph.D. in Financial Mathematics
Dr. Vance specializes in time value of money calculations, ensuring the formulas for compounding and discounting are accurate for long-term financial planning.

Use the authoritative **Future Value Calculator** to project the value of an investment over time. Enter any three variables—Future Value, Principal (Current Savings), Annual Rate, or Time in Years—to solve for the remaining unknown value.

F: Target Future Value ($\mathbf{FV}$, $)

P: Principal / Present Value ($\mathbf{PV}$, $)

V: Annual Interest Rate ($\mathbf{r}$, %)

Q: Time in Years ($\mathbf{n}$, Years)

Future Value Formula (Lump Sum)

Core Relationship: Future Value $= \text{Present Value} \times (1 + \text{Rate})^{\text{Time}}$

$$ FV = PV \times (1 + r)^n $$

The four solution formulas (Where $\mathbf{r}$ is decimal and compounding is annual):

$\mathbf{FV}$ (F) $= P \times (1 + r)^n$

$\mathbf{PV}$ (P) $= FV / (1 + r)^n$

$\mathbf{r}$ (Rate, V) $= \left(\left(\frac{FV}{PV}\right)^{\frac{1}{n}} – 1\right) \times 100$

$\mathbf{n}$ (Time, Q) $= \frac{\ln(FV / PV)}{\ln(1 + r)}$

Formula Source: Investopedia

Formula Variables

F ($\mathbf{FV}$): The value of the asset at a specified date in the future (the target value).
P ($\mathbf{PV}$): The Present Value or Principal amount invested today.
V ($\mathbf{r}$): The Annual Interest Rate (rate of return or discount rate).
Q ($\mathbf{n}$): The number of time periods (years) the money is invested or borrowed.

Related Calculators

What is Future Value (FV)?

Future Value (FV) is the value of a current asset at a specified date in the future, based on an assumed growth rate. The concept is central to the time value of money and forms the basis of all investment and financial planning. Calculating the FV allows you to forecast how much money an investment will be worth given its risk and expected rate of return.

The calculation is driven by compounding—the process where the earnings from the investment are reinvested, earning their own returns over time. The longer the time period ($\mathbf{n}$) and the higher the interest rate ($\mathbf{r}$), the greater the effect of compounding, leading to a significantly higher Future Value. This is why financial experts stress starting to save and invest early.

How to Calculate Required Time in Years (Example)

Let’s find the required time ($\mathbf{n}$, Q) to grow a Principal ($\mathbf{PV}$) of \$5,000 to a Future Value ($\mathbf{FV}$) of \$15,000 at an Annual Rate ($\mathbf{r}$) of 8.0\%.

Step 1: Convert Rate to Decimal and Calculate Growth Factor
Annual Rate $r = 8.0\% / 100 = 0.08$. Growth Factor $(\mathbf{1 + r}) = 1.08$.
Step 2: Calculate Required Multiple (FV/PV)
Multiple $= \$15,000 / \$5,000 = 3.0$ times.
Step 3: Apply the Time Formula ($\mathbf{n = \ln(FV/PV) / \ln(1+r)}$)
$n = \ln(3.0) / \ln(1.08) \approx 13.73$ years.
Step 4: Determine the Required Time
The calculation yields a required Time ($\mathbf{n}$) of **13.73 years** to achieve the target Future Value.

Frequently Asked Questions (FAQ)

What is the difference between FV and PV?

Future Value (FV) is the worth of money at a date in the future, whereas Present Value (PV) is the current worth of that money, discounted back to the present day. They are inverses of each other, separated by the discount rate and time.

Does this calculator include regular contributions?

No, this calculator uses the lump-sum formula, assuming a single initial investment (Principal, PV). If you plan to make periodic contributions, you should use the Related Retirement Savings Calculator, which uses the Future Value of an Annuity formula.

What is the Rule of 72?

The Rule of 72 is a quick, approximate way to estimate the number of years ($\mathbf{n}$) required for an investment to double in value: $n \approx 72 / r$. For example, at an 8% rate, it takes about $72/8 = 9$ years to double.

How does compounding frequency affect FV?

This calculator assumes annual compounding. If compounding were more frequent (e.g., monthly), the Future Value would be slightly higher, as interest earns interest more often. The rate and time would need to be adjusted: $r/m$ and $n \times m$, where $m$ is the frequency.

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