What Is the Time Value of Money?
The time value of money (TVM) is a foundational concept in finance: a dollar today is worth more than a dollar in the future because today's dollar can be invested to earn a return. TVM calculations are used in investment analysis, retirement planning, loan evaluation, and business valuation.
The four core TVM variables are: Present Value (PV), Future Value (FV), Interest Rate (r), and Number of Periods (n). Given any three, you can solve for the fourth.
TVM Formulas
FV = PV × (1 + r/m)^(n×m)
PV = FV / (1 + r/m)^(n×m)
r = (FV/PV)^(1/n) − 1 (annual, no payments)
n = ln(FV/PV) / ln(1 + r)
Where:
PV = Present Value
FV = Future Value
r = Annual interest rate (decimal)
n = Number of years
m = Compounding periods per year