Time Value of Money Calculator
Calculate Present Value or Future Value of money.
Understand how inflation and interest rates affect the value of money over time.
Time Value of Money (TVM) is the foundational principle of finance: a dollar today is worth more than a dollar in the future, because money held now can be invested to generate returns.
Five core TVM formulas:
Future Value (FV):
FV = PV × (1 + r)^n
Present Value (PV):
PV = FV / (1 + r)^n
Future Value of an Annuity (regular payments):
FV_annuity = PMT × [(1 + r)^n − 1] / r
Present Value of an Annuity:
PV_annuity = PMT × [1 − (1 + r)^−n] / r
Payment required for a given FV or PV (PMT):
PMT = PV × [r(1+r)^n] / [(1+r)^n − 1]
Variable definitions:
- PV = present value (lump sum today)
- FV = future value (amount at end of period)
- PMT = periodic payment amount
- r = interest rate per period (annual rate ÷ compounding periods)
- n = total number of periods
Worked example — Lump sum growth: Invest $10,000 today at 8% annually for 20 years:
- FV = $10,000 × (1.08)^20 = $10,000 × 4.661 = $46,610
Worked example — Monthly savings goal: Save $500/month at 6%/year for 30 years:
- r = 0.06/12 = 0.005 per month | n = 360 months
- FV = $500 × [(1.005)^360 − 1] / 0.005 = $502,257
Compounding frequency matters: $10,000 at 6% for 10 years:
- Annual compounding: $17,908
- Monthly compounding: $18,194
- Daily compounding: $18,220