This Rate of Return Calculator accurately determines the growth factor of an investment over time, based on the fundamental time value of money principle.
Welcome to the **Rate of Return Calculator**. This tool uses the compound interest formula to determine any of the four core variables: Present Value ($PV$), Future Value ($FV$), Rate of Return ($R$), or Time in Years ($T$). The Rate of Return is a critical metric for evaluating the performance and potential growth of any investment. Input any three of the variables to solve for the missing one.
Rate of Return Calculator
Rate of Return Formula
The core Time Value of Money equation (Annual Compounding) is:
$$ FV = PV \times (1 + R)^T $$
1. Solve for Future Value (FV):
$$ FV = PV \times (1 + R)^T $$
2. Solve for Present Value (PV):
$$ PV = \frac{FV}{(1 + R)^T} $$
3. Solve for Rate of Return (R):
$$ R = \left(\frac{FV}{PV}\right)^{\frac{1}{T}} – 1 $$
4. Solve for Time (T):
$$ T = \frac{\ln(FV / PV)}{\ln(1 + R)} $$
Formula Source: Investopedia – Rate of Return
Variables Explained
- PV – Present Value: The initial principal investment or the current value of a future sum.
- FV – Future Value: The ending value of the investment after the time period, including all interest/returns.
- R – Rate of Return: The annual percentage rate of growth/interest, expressed as a decimal in the formula (e.g., 5% = 0.05).
- T – Time Period: The length of time in years over which the investment is compounded.
Related Calculators
What is the Rate of Return?
The Rate of Return (ROR) is the gain or loss on an investment over a specified period, expressed as a percentage of the investment’s cost. It is a fundamental metric in finance used to measure how profitably an investment is growing. A positive ROR means the investment has made money, while a negative ROR indicates a loss.
Understanding ROR is crucial for making informed investment decisions. When comparing different investment opportunities, investors typically use the annualized ROR to normalize performance across varying time periods. For this calculator, the rate ($R$) is assumed to be compounded annually for simplicity, though real-world rates can be compounded monthly or daily.
This calculator uses the compound interest formula, which is the most common way to determine the average annualized rate of return necessary to achieve a specific future value from a known present value over a set period.
How to Calculate Rate of Return (Example)
Assume an initial investment (**PV**) of **$5,000** grows to a final value (**FV**) of **$7,000** over a time period (**T**) of **5 years**.
- Determine the Missing Variable: Rate of Return ($R$) is missing.
- Apply Formula: $R = (FV / PV)^{\frac{1}{T}} – 1$.
- Substitute Values: $R = (\$7,000 / \$5,000)^{\frac{1}{5}} – 1$.
- Calculate Power: $(1.4)^{\frac{1}{5}} \approx 1.0696$.
- Determine R: $R = 1.0696 – 1 = 0.0696$.
- Convert to Percentage: $R = 6.96\%$. The required Rate of Return is **6.96%**.
Frequently Asked Questions (FAQ)
The Annual Percentage Yield (APY) includes the effect of compounding, whereas a simple Rate of Return may sometimes refer to the basic percentage gain without accounting for time or compounding frequency. This calculator assumes annual compounding.
Why is it important to use the Future Value (FV) rather than just profit?Using the FV ensures the calculation of the ROR is accurately linked to the time value of money principle. The FV is the total value, including both the initial investment and all earned returns.
Can the Rate of Return be negative?Yes. If the Future Value ($FV$) is less than the Present Value ($PV$), the ratio $FV/PV$ will be less than 1, resulting in a negative Rate of Return, which indicates a loss on the investment.
How does inflation affect the Rate of Return?The rate calculated here is the nominal ROR. To find the real ROR, you would subtract the inflation rate from the nominal rate, which gives the true increase in purchasing power.