What is Present Value?
Present value (PV) is one of the most important ideas in finance and accounting: it converts a future sum of money into what that money is worth today, using a discount rate. Investors, lenders, and accountants use PV to compare cash flows that happen at different points in time.
Present value is the current worth of a future amount of money, discounted back at a required rate of return: PV = FV / (1 + r)^n, where r is the discount rate and n is the number of periods.
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Step-by-step worked examples
What is the present value of $10,000 to be received in 10 years, at a discount rate of 5%?
PV = FV / (1+r)^n PV = 10,000 / (1.05)^10 PV = 10,000 / 1.62889 PV ≈ $6,139.13
Find the present value of $5,000 due in 5 years at an 8% discount rate.
PV = 5,000 / (1.08)^5 PV = 5,000 / 1.46933 PV ≈ $3,402.92
A bond pays $20,000 in 20 years. At a 3% discount rate, what is it worth today?
PV = 20,000 / (1.03)^20 PV = 20,000 / 1.80611 PV ≈ $11,074.68
Flashcards
Quick quiz
Q1.What is the present value of $1,000 received in 1 year at a 10% discount rate?
Q2.In the PV formula PV = FV/(1+r)^n, what does r represent?
Q3.As the discount rate increases, present value…
Q4.Why is $1,000 today worth more than $1,000 in 5 years?
The full card deck, worked steps and AI-tutor support for “What is Present Value?” are in Notek — study by hand before your exam.
Common mistakes
Treating $1,000 today and $1,000 in 10 years as equal. — Correct: They are not equal — money today is worth more due to its earning potential (time value of money).
Forgetting to convert an annual rate to match the compounding period. — Correct: Match r and n to the same period (e.g., use a monthly rate with monthly periods).
Using a discount rate of 5 instead of 0.05 (or 5%) in the formula. — Correct: Convert percentages to decimals (5% = 0.05) before applying the exponent.
Adding FV and the discount instead of dividing by (1+r)^n. — Correct: PV always divides FV by the compound discount factor (1+r)^n.
FAQ
What is present value?
Present value is the current worth of a future sum of money, calculated by discounting it back at a specific rate: PV = FV/(1+r)^n.
What is the present value formula?
PV = FV / (1 + r)^n, where FV is the future amount, r is the discount rate, and n is the number of periods.
How do you calculate present value?
Divide the future value by (1 plus the discount rate) raised to the power of the number of periods: PV = FV/(1+r)^n.
What are examples of present value in real life?
Valuing a bond's future payments, pricing a business acquisition, or deciding whether a lottery lump sum beats the annuity option.