Time value of money (TVM) is the foundational financial concept that a dollar available today is worth more than a dollar in the future, because the dollar today can be invested and earn a return.
Five TVM variables (financial calculator): - N = number of periods - I/Y = interest rate per period - PV = present value - PMT = periodic payment (annuity) - FV = future value
Know any four → solve for the fifth.
Key formulas:
Future Value (single sum): > FV = PV × (1 + r)^n
Present Value (single sum): > PV = FV ÷ (1 + r)^n
Future Value of an annuity: > FV = PMT × [(1 + r)^n − 1] ÷ r
Present Value of an annuity: > PV = PMT × [1 − (1 + r)^(−n)] ÷ r
Annuity due vs. ordinary annuity: - Ordinary annuity: Payments at END of period (most common). - Annuity due: Payments at BEGINNING of period (e.g., rent, insurance). FV and PV are each × (1 + r) larger.
Rule of 72: Approximate years to double money = 72 ÷ interest rate. (Example: 8% → 72 ÷ 8 = 9 years to double.)
Compounding frequency: More frequent compounding (daily vs. annual) → higher effective annual rate (EAR). > EAR = (1 + nominal rate/m)^m − 1
> Exam tip: TVM is the backbone of financial planning. For the CFP® exam, you must be proficient with a financial calculator (HP 12C or BAII Plus). Know the difference between ordinary annuity and annuity due — a common source of errors.