Time Value of Money Calculator

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