What is the Time Value of Money?
The time value of money is the financial principle that a sum of money today is worth more than the same sum in the future, because it can be invested to earn a return. It underlies compound interest, present value, and future value calculations used throughout finance and accounting.
The time value of money states that money available now is worth more than the same amount later, because of its earning potential; future value FV = PV × (1 + r)^n grows a present sum PV at rate r over n periods.
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Step-by-step worked examples
You invest $10,000 today at an annual interest rate of 5%, compounded annually. What will it be worth in 10 years?
FV = PV × (1+r)^n = 10,000 × (1.05)^10 (1.05)^10 ≈ 1.6289 FV ≈ 10,000 × 1.6289 = $16,289
How much would $5,000 grow to in 6 years at an 8% annual rate?
FV = 5,000 × (1.08)^6 (1.08)^6 ≈ 1.5869 FV ≈ 5,000 × 1.5869 ≈ $7,934.37
You want $20,000 in 5 years and can earn 6% annually. How much must you invest today (present value)?
FV = PV × (1+r)^n → PV = FV / (1+r)^n PV = 20,000 / (1.06)^5 (1.06)^5 ≈ 1.3382 PV ≈ 20,000 / 1.3382 ≈ $14,946
Flashcards
Quick quiz
Q1.You invest $8,000 at 4% annual interest for 5 years. What is the approximate future value?
Q2.What does a higher interest rate do to future value, holding PV and n constant?
Q3.What is the present value of $12,000 to be received in 3 years at a 10% discount rate?
Q4.Which factor does NOT appear in the future value formula FV = PV×(1+r)^n?
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Common mistakes
Treating a future dollar as equal in value to a present dollar. — Correct: Money available today is worth more due to its earning potential — always discount future amounts to compare fairly.
Using simple interest math when the problem specifies compounding. — Correct: For compound interest, use FV = PV×(1+r)^n, not FV = PV×(1+r×n).
Forgetting to convert the interest rate to match the compounding period (e.g., using an annual rate with monthly compounding). — Correct: Match r and n to the same period length — e.g., divide annual rate by 12 and multiply years by 12 for monthly compounding.
Confusing present value and future value formulas. — Correct: FV grows a present sum forward; PV discounts a future sum backward — they are inverses: PV = FV/(1+r)^n.
FAQ
What is the time value of money?
It's the concept that money available now is worth more than the same amount in the future due to its potential to earn interest or investment returns.
What is the time value of money formula?
Future value FV = PV × (1 + r)^n, where PV is present value, r is the periodic interest rate, and n is the number of periods.
What are examples of the time value of money?
Choosing to receive $1,000 today rather than $1,000 in five years, because today's $1,000 can be invested and grow, is a classic example.
How do you calculate the time value of money?
Use FV = PV×(1+r)^n to find future value, or rearrange to PV = FV/(1+r)^n to find present value, given a rate r and number of periods n.