Present Value Calculator

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Reviewed by: Dr. Hannah Lee, CPA, Financial Modeler
Dr. Lee is a Certified Public Accountant specializing in corporate valuation and time value of money calculations, ensuring the accuracy of all present value computations.

Use the authoritative **Present Value Calculator** to instantly determine the current worth of a future sum of money. Enter any three variables—Future Value, Annual Rate, Time in Years, or Present Value—to solve for the remaining unknown variable.

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

P: Annual Interest/Discount Rate ($\mathbf{r}$, %)

V: Time Period ($\mathbf{n}$, Years)

Q: Present Value ($\mathbf{PV}$) ($)

Present Value Formula

Core Present Value Relationship (Single Lump Sum):

$$ PV = \frac{FV}{(1 + r)^n} $$

The four solution formulas:

PV (Q) $= \text{FV} / (1 + r)^n$

FV (F) $= \text{PV} \times (1 + r)^n$

r (Rate, P) $= [(FV / PV)^{1/n} – 1] \times 100$

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

Formula Source: Investopedia

Formula Variables

F ($\mathbf{FV}$ – Future Value): The amount of money to be received or reached at the end of the term.
P ($\mathbf{r}$ – Annual Rate): The annual discount rate or expected rate of return (as a decimal in formulas).
V ($\mathbf{n}$ – Time): The number of time periods (years) until the future value is realized.
Q ($\mathbf{PV}$ – Present Value): The value today of the future lump sum amount.

Related Calculators

What is Present Value?

Present Value (PV) is the current worth of a future sum of money or stream of cash flows, given a specified rate of return. The core concept is that money available today is worth more than the same amount in the future due to its potential earning capacity. This principle, known as the Time Value of Money (TVM), is essential for investment analysis, financial planning, and business valuation.

The process of finding the Present Value is called **discounting**, which involves reducing the Future Value (FV) by the annual discount rate ($r$) for each time period ($n$). The higher the discount rate or the longer the time period, the lower the Present Value will be. This calculator specifically focuses on the Present Value of a single lump sum, rather than a stream of payments (annuity).

How to Calculate Required Rate (Example)

Let’s find the Annual Rate (P) required for a Present Value (Q) of \$10,000 to grow to a Future Value (F) of \$15,000 in 10 years (V).

Step 1: Determine Known Variables
$FV = \$15,000$. $PV = \$10,000$. $n = 10$ years.
Step 2: Calculate the Growth Factor
The total growth factor is $FV / PV = \$15,000 / \$10,000 = 1.5$.
Step 3: Apply the Rate Formula ($\mathbf{r = [(FV / PV)^{1/n} – 1] \times 100}$)
Annual Growth Factor $= (1.5)^{1/10} \approx 1.0413797$.
Step 4: Determine the Annual Rate
Rate ($r$) $= (1.0413797 – 1) \times 100 \approx 4.14\%$ per year.

Frequently Asked Questions (FAQ)

What is a Discount Rate?

The discount rate ($r$) is the rate used to calculate the present value of future cash flows. It represents the required rate of return that an investor would demand, or the opportunity cost of investing elsewhere with a similar risk profile.

How is Present Value used in real estate or business?

In real estate, PV helps determine the current fair price of a property based on its expected future rental income. In business, it’s used in capital budgeting (Net Present Value or NPV) to decide whether an investment project is financially worthwhile.

What happens to PV if the time period (n) increases?

If the time period ($n$) increases, the Present Value (PV) decreases, assuming the rate ($r$) is positive. This is because the discounting effect is compounded over more years, making the future sum worth less today.

Does this calculator handle monthly compounding?

This simplified calculator assumes annual compounding (and discounting). For monthly compounding, the rate ($r$) should be divided by 12, and the time period ($n$) should be multiplied by 12.

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