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.

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