Time Value of Money (TVM) — why $1 today is worth more than $1 tomorrow

The time value of money is a simple idea with huge consequences: money can earn a return. If you can invest cash (even at a modest interest rate), a dollar today can become more than a dollar in the future. That’s why financial decisions almost always involve “discounting” future cash flows back to today, or “compounding” today’s money forward into the future.

This calculator is designed to be practical: you can solve for future value (FV), present value (PV), interest rate, or number of periods. You can also include a recurring payment (PMT) (like a monthly contribution or withdrawal) and choose whether payments happen at the end of each period (ordinary annuity) or the beginning (annuity due). It’s essentially the “engine” behind many other tools: compound interest, savings goals, retirement planning, and loan math.

• Compounding forward (FV from PV): FV = PV × (1 + r)n
• Discounting back (PV from FV): PV = FV ÷ (1 + r)n

Where: PV is the value today, FV is the value in the future, r is the periodic interest rate (per period, not per year), and n is the number of periods. If your rate is expressed as an annual nominal rate, and compounding happens multiple times per year, the periodic rate is typically: r = annualRate ÷ compoundingPerYear, and the number of periods becomes n = years × compoundingPerYear.

Many real-world situations include regular contributions (saving) or withdrawals (spending). When payments are at the end of each period (ordinary annuity), a common formula is:

• Future value with payments: FV = PV(1 + r)n + PMT × [((1 + r)n − 1) ÷ r]
• Present value with payments: PV = FV ÷ (1 + r)n − PMT × [(1 − (1 + r)−n) ÷ r]

If payments happen at the beginning of the period (annuity due), the payment portions get multiplied by (1 + r) because each payment earns one extra period of growth. This is why contributing at the beginning of the month usually beats contributing at the end.

Example 1 — compounding: Suppose you invest $10,000 for 10 years at 7% annually (compounded once per year). Your FV is 10,000 × 1.0710 ≈ $19,671. That’s the classic “money grows over time” story.

Example 2 — discounting: If someone promises you $20,000 in 10 years and your opportunity cost is 7%, the PV is 20,000 ÷ 1.0710 ≈ $10,168. In other words, $20k in ten years “feels like” about $10k today at a 7% discount rate.

Example 3 — regular contributions: Contribute $300/month for 20 years at 6% annually compounded monthly. Here, r = 0.06/12 and n = 20×12. Even if you start from $0 PV, the payment stream compounds into a meaningful balance. This is why consistency matters more than “perfect timing” for many savers.

• Pick what you want to solve for: Future Value, Present Value, Rate, or Time.
• Enter known values: fill in PV, FV, years, and annual rate as applicable.
• Set compounding: yearly, quarterly, monthly, weekly, or daily.
• Optional payments: add a recurring payment and choose end vs beginning timing.
• Calculate: the result panel explains the output and shows APY.

• Mixing annual and periodic rates: If compounding is monthly, your periodic rate is annual/12.
• Forgetting number of periods: 20 years monthly is 240 periods, not 20.
• APR vs APY confusion: APY includes compounding; the calculator shows both.
• Payment timing: “Beginning of period” grows slightly faster (annuity due).

• Is TVM only for investing?

  No. TVM applies to loans, mortgages, business projects, and any decision with cash at different times.

• What rate should I use?

  Use your opportunity cost: a reasonable expected return for the risk level, or a conservative target rate.

• What’s the difference between nominal and effective rate?

  Nominal is the stated annual rate. Effective (APY) is what you actually earn after compounding.

• Why does solving for rate use iteration?

  When payments are included, the rate appears inside powers and series terms—so we use a safe numeric search.

• Does inflation matter?

  Yes. Pair this with Inflation Impact / Real Return tools to measure purchasing power.

Disclaimer: This tool provides educational estimates. Real returns vary, taxes and fees may apply, and investing involves risk.

TVM terms in plain English

• Compounding: earning “interest on interest” over time.
• Discounting: translating future money into today’s value.
• Nominal rate: the stated annual rate.
• Effective rate (APY): the “true” annual growth after compounding.
• Annuity: a stream of equal payments (PMT).
• Annuity due: payments at the beginning of each period.

• Use Future Value for a simple PV → FV.
• Use Present Value to discount a lump sum.
• Use Inflation Impact for purchasing power.
• Use Compound Interest for growth basics.