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 that amortizes a present value (PMT): PMT = PV × [r(1+r)^n] / [(1+r)^n − 1]

The calculator on this page handles the first two formulas, the lump-sum pair, at annual compounding. The annuity and payment formulas are here as reference for when you need them.
For those, and for anything with regular payments or non-annual compounding, use the TVM solver. It takes all five variables, solves for whichever one you leave blank, and agrees with this page to the cent on the lump-sum cases.

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

Notice how little the last step buys. Going from annual to monthly is worth $286 over ten years. Going from monthly to daily is worth $26. The gap between daily and continuous compounding is smaller still, which is why arguing about compounding frequency is usually a waste of an afternoon and arguing about the rate never is. The calculator here uses annual compounding, so if your account compounds monthly, expect the real figure to land slightly above what it shows.

Where people get this wrong

The discount rate is not the inflation rate and it is not your bank’s savings rate. It is what the money could earn in its next-best use, which for a business is usually its cost of capital and for an individual is usually whatever a broad index fund has returned. Pick it too low and every future payment looks valuable. Pick it too high and no long-term investment ever justifies itself. Most bad capital decisions trace back to that single number rather than to any of the arithmetic around it.