Time value of money — definition and examples

What is time value of money?

Time value of money (TVM) is a principle stating that money available today is worth more than the same amount in the future. Why? Because today you can invest it and earn interest on it.

Quick Answer

The time value of money (TVM) holds that one złoty today is worth more than one złoty tomorrow, because money available now can be invested to earn a return. Three forces drive it: investment potential, inflation eroding purchasing power, and the risk that a future payment never arrives. It is calculated with two mirror formulas — future value FV = PV × (1 + r)ⁿ for compounding forward and present value PV = FV / (1 + r)ⁿ for discounting backward — underpinning investing, loan valuation and retirement planning.

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Why one złoty today > one złoty tomorrow?

Three reasons:

1. Investment potential — you can invest and earn a return
2. Inflation — the purchasing power of money decreases over time
3. Risk — future payment is uncertain

Formula — Future Value

FV = PV × (1 + r)ⁿ

• FV — future value
• PV — present value
• r — rate of return (annually)
• n — number of years

Example

1,000 PLN invested at 8% annually for 20 years:

FV = 1,000 × (1.08)²⁰ = 4,661 PLN

The same amount in an account with 0% interest after 20 years is still 1,000 PLN — but worth less in real terms due to inflation.

Formula — Present Value

PV = FV / (1 + r)ⁿ

What is today's worth of 10,000 PLN that you will receive in 10 years (with a 6% discount rate)?

PV = 10,000 / (1.06)¹⁰ = 5,584 PLN

Practical applications

• Investing — the earlier you start, the more you earn (compound interest)
• Comparing offers — 100,000 PLN today vs 120,000 PLN in 5 years? TVM gives the answer
• Loan valuation — 500 PLN/month for 30 years is much more than the nominal sum
• Retirement planning — how much you need to save today to have X in 30 years

Rule of 72

A quick way to estimate how many years it takes to double your money:

Years to double ≈ 72 / rate of return (%)

• At 6% → 72/6 = 12 years
• At 8% → 72/8 = 9 years
• At 12% → 72/12 = 6 years

How can Freenance help

Freenance uses the TVM principle in its calculators — portfolio projections, FIRE calculator and runway. You see how your money can grow over time and make decisions based on mathematics, not intuition.

👉 Calculate future value with Freenance — freenance.io

FAQ

What is the difference between present value and future value?

Present value (PV) is the current worth of a future cash flow discounted at a chosen rate, while future value (FV) is what today's amount will grow to after compounding over time. Both are two sides of the same TVM equation — discounting moves money backwards in time, compounding moves it forward.

Why is discounting necessary when comparing investments?

Money received later is worth less than money received today because of inflation, investment opportunity cost and uncertainty. Discounting normalises future cash flows to today's złoty so that two offers with different timing can be compared on equal terms.

What discount rate should I use for personal financial planning?

There is no single correct rate — a common approach is to use your realistic long-term portfolio return (for example a diversified equity benchmark net of fees) or the cost of capital you would otherwise pay. The lower the rate, the more weight the calculation puts on distant cash flows.

Does the Rule of 72 work for any interest rate?

The Rule of 72 is a useful approximation for typical rates between roughly 4% and 12%; outside that range the estimate becomes less accurate. For precise planning use the full formula FV = PV × (1 + r)ⁿ rather than the shortcut.

How does inflation interact with the time value of money?

TVM formulas can be calculated in nominal terms (using the quoted rate) or in real terms (using the rate minus inflation). For long-horizon goals such as retirement, working in real terms gives a clearer picture of actual purchasing power.

Related Articles

• Opportunity cost (koszt alternatywny) — definicja
• Real rate of return (realna stopa zwrotu) — definicja
• Nominal rate (nominalna stopa zwrotu) — definicja