David is a Chartered Financial Analyst with 15 years of experience in investment analysis and financial planning.
This 4-in-1 Present Value (PV) calculator helps you find the value of a future sum of money today. Enter any three variables—Present Value, Future Value, Annual Rate, or Term—to solve for the fourth.
Present Value Calculator
Present Value Formulas
PV = FV / (1 + r)^t
Solve for Future Value (FV):
FV = PV * (1 + r)^t
Solve for Rate (r):
r = ( (FV / PV)^(1/t) ) – 1
Solve for Term (t):
t = ln(FV / PV) / ln(1 + r)
Formula Variables
- (PV) Present Value: The starting amount of money; what a future sum is worth today.
- (FV) Future Value: The total value of the investment at the end of the term.
- (R) Annual Rate: The annual interest rate (or discount rate), entered as a percentage (e.g., 8 for 8%).
- (T) Term (Years): The total number of years the money is invested.
- (r): Rate per period (R / 100)
- (t): Number of periods (T)
Related Calculators
What is Present Value?
Present Value (PV) is the financial concept of “a dollar today is worth more than a dollar tomorrow.” It tells you the current worth of a future sum of money, given a specific rate of return (or “discount rate”). It is the opposite of Future Value (FV), which calculates what today’s money will be worth in the future.
This concept is vital for financial planning and investment analysis. For example, if someone promises to give you $20,000 in 10 years, the present value of that promise is much less than $20,000. Why? Because you could take a smaller amount of money today, invest it, and grow it to $20,000 in 10 years yourself. The Present Value calculator finds exactly what that smaller amount is.
This process of calculating present value is often called “discounting.” The interest rate (R) is used as the “discount rate” to determine how much the future sum should be reduced to find its value today.
How to Calculate Present Value (Example)
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Identify Your Goal
You want to have $20,000 (FV) in 10 years (T) for a down payment. You believe you can earn an 8% (R) annual return on your investments. You need to find how much money to invest today (PV).
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Find the Rate (r) and Term (t)
Rate (r) = 8% / 100 = 0.08
Term (t) = 10 years -
Apply the Present Value Formula
The formula is: PV = FV / (1 + r)^t
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Calculate the Value
PV = $20,000 / (1 + 0.08)^10
PV = $20,000 / (1.08)^10
PV = $20,000 / 2.15892 -
Final Result
You would need to invest $9,263.87 today (PV) to have $20,000 in 10 years.
Frequently Asked Questions (FAQ)
The “discount rate” is just another name for the interest rate (R) when you are solving for Present Value. It’s the rate used to “discount” a future sum back to its value in today’s terms.
How do I find how long it will take for my money to grow?You can use this calculator. Enter your Present Value (PV) (how much you have now), your target Future Value (FV), and the Annual Rate (R) you expect to earn. Leave the “Term (T)” field blank and click “Calculate.” The result will show you how many years it will take to reach your goal.
What’s the difference between Present Value and Future Value?Present Value (PV) is what a future amount is worth today. Future Value (FV) is what a current amount will be worth in the future. They are two sides of the same coin, using the same compound interest formula rearranged to solve for a different variable.
Why is Present Value important for loans?Present Value is the core concept of an amortizing loan (like a mortgage). The loan amount you receive today is the “Present Value.” Your series of future monthly payments, when discounted back to today, are equal to that present value. This calculator helps you understand that time-value-of-money relationship.