Dr. Vance specializes in time value of money, investment modeling, and compound growth analysis.
The **Future Value of Single Sum Calculator** determines the total value of a single lump-sum investment or deposit at a specified point in the future, based on compound interest. This versatile four-variable calculator solves for any missing input: **Future Value ($FV$)**, **Present Value ($PV$)**, **Interest Rate ($R$)**, or the **Number of Periods ($N$)**. **Input any three of the four core variables** to find the missing one.
Future Value of Single Sum Calculator
Future Value of Single Sum Formulas
The Future Value of a Single Sum (FVSS) is the foundation of compound interest. It measures the value of money invested today ($PV$) after a period of growth ($N$) at a specific interest rate ($R$).
Note: $r$ is the decimal rate per period ($R_{percent}/100$).
Formula Source: Investopedia: Future Value
Variables Explained
The calculation uses these key Time Value of Money variables:
- Future Value (FV): The final balance after $N$ periods, including compound interest ($).
- Present Value (PV): The initial principal amount or lump-sum investment ($).
- Interest Rate (R): The periodic interest rate (e.g., annual or monthly rate) (%).
- Number of Periods (N): The total number of compounding periods (e.g., years, months).
Related Calculators
Compare future growth models using these related tools:
- Present Value Calculator
- Compound Annual Growth Rate Calculator
- Effective Annual Rate Calculator
- Future Value of Annuity Calculator
What is Future Value of a Single Sum?
The **Future Value of a Single Sum (FVSS)** is a core concept in finance used to project the growth of an initial capital amount. It assumes the interest earned in each period is reinvested (compounded), allowing the investment to grow exponentially. This is the simplest application of compound interest, where a single deposit grows over time without any subsequent additions or withdrawals.
This metric is critical for long-term financial planning, such as estimating how much a current lump sum will be worth at retirement, or how much an initial business investment will yield after several years of growth.
How to Calculate FVSS (Example)
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Identify Components:
You invest a $\mathbf{PV}$ of $\mathbf{\$1,000}$ at a $\mathbf{R}$ of $\mathbf{7\%}$ (0.07) for $\mathbf{N}$ of $\mathbf{5 \ years}$.
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Apply the Formula:
$$ FV = \$1,000 \cdot (1 + 0.07)^5 $$
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Calculate the Compounding Factor:
$(1.07)^5 \approx \mathbf{1.40255}$
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Determine the Future Value:
$$ FV = \$1,000 \times 1.40255 \approx \mathbf{\$1,402.55} $$
Frequently Asked Questions (FAQ)
A: The more frequently interest is compounded (e.g., monthly vs. annually), the higher the final Future Value will be, even if the Annual Rate ($R$) remains the same.
A: You use the Present Value (PV) formula when you know the future value you need and want to find out how much you must invest today (PV) to reach that goal.
A: Yes, in periods of deflation or certain negative interest rate policies, the rate can be negative. A negative rate will result in the Future Value being less than the Present Value.
A: The total interest earned is simply the difference between the final Future Value (FV) and the initial Present Value (PV): $I = FV – PV$.