What is the Time Value of Money?
The time value of money (TVM) is the 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 nearly every financial decision, from loans to retirement savings.
Time value of money means present cash is worth more than the same amount in the future because of its earning potential; it's captured by the formula FV = PV × (1 + r)^n, linking present value, future value, rate and time.
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Step-by-step worked examples
You invest $5,000 today at 7% annual interest. What is it worth in 10 years?
FV = PV × (1+r)^n FV = 5000 × (1.07)^10 FV = 5000 × 1.9672 ≈ $9,835.76
How much must you deposit today (PV) to have $20,000 in 8 years at 5% interest?
Rearrange: PV = FV / (1+r)^n PV = 20000 / (1.05)^8 1.05^8 ≈ 1.4775 PV = 20000 / 1.4775 ≈ $13,536.90
Which is worth more: $1,000 received today, or $1,000 received in 3 years, if the discount rate is 4%?
Compare via present value of the future amount PV of $1,000 in 3 years = 1000 / (1.04)^3 1.04^3 = 1.124864 PV ≈ $889.00, which is less than $1,000 today So $1,000 today is worth more
Flashcards
Quick quiz
Q1.$1,000 today at 5% annual interest is worth how much in 1 year?
Q2.Which factor is NOT part of the TVM formula FV = PV(1+r)^n?
Q3.What does 'discounting' a future cash flow mean?
Q4.All else equal, a higher discount rate makes a future cash flow's present value…
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Common mistakes
Treating $1,000 now and $1,000 in 5 years as equal. — Correct: They are NOT equal — money today can earn interest, so it's worth more than the same nominal amount later.
Forgetting to convert an annual rate when compounding periods differ. — Correct: Match r and n to the same period (e.g. use a monthly rate with monthly periods).
Confusing present value and future value formulas. — Correct: FV = PV(1+r)^n grows money forward; PV = FV/(1+r)^n discounts it backward.
Ignoring the interest rate when comparing cash flows at different times. — Correct: You must apply a discount/interest rate to make cash flows at different times comparable.
FAQ
What is the time value of money?
It's the principle that a sum of money is worth more now than the same sum in the future, because of its potential to earn interest.
What is the time value of money formula?
FV = PV × (1 + r)^n, where PV is present value, r is the rate per period and n is the number of periods.
How do you calculate the time value of money?
Multiply the present value by (1 + rate)^periods to find future value, or divide a future value by the same factor to find present value.
What are examples of the time value of money?
Choosing a lump sum today over a larger sum later, pricing a bond, or deciding whether to invest now versus save later.