Time Value of Money — Why a Euro Today is Worth More Than Tomorrow

The time value of money (TVM) is the foundational principle of finance: a euro available today is worth more than a euro promised in the future. This is not simply because of inflation, but because money available now can be invested to generate returns, making the future euro genuinely worth less in present terms. Every financial decision — loan pricing, investment valuation, pension planning, and business appraisal — is built on this principle.

time-value-of-money tvm present-value future-value discounting finance

Quick reference

Future value

PV x (1+r)^n

What today's money grows to

Present value

FV / (1+r)^n

What future money is worth today

Discount rate

Opportunity cost

Rate forgone by waiting

Key insight

Time costs money

Receiving later is worth less

Why a euro today is worth more than a euro in the future

Three reasons explain why money today is more valuable than the same amount in the future.

First, opportunity cost. Money available now can be invested and earn a return. If you can earn 5% per year, 1.000 today becomes 1.050 in one year. A promise of 1.000 in one year is worth only 1.000/1,05 = 952,38 today — because 952,38 invested at 5% for one year produces exactly 1.000.

Second, inflation. The purchasing power of money decreases over time as prices rise. 1.000 in 10 years will buy less than 1.000 today if there is positive inflation. Even with zero inflation, the first reason alone makes future money worth less.

Third, risk. A promised future payment carries uncertainty. The payer may default. Conditions may change. Receiving 1.000 with certainty today is preferable to a promise of 1.000 in one year, even ignoring investment opportunity, because the future payment has additional uncertainty.

These three factors combine to make the present value of any future cash flow less than its nominal future amount.

Future value formula

Formula

FV = PV \times (1 + r)^n

Future value equals present value multiplied by one plus the rate per period, raised to the number of periods. This is the same as the compound interest formula. It answers: what will this money be worth in the future if invested at rate r for n periods?

FVFuture value — the value of the money at a future point in time

PVPresent value — the value of the money today

rRate of return per period as a decimal — the opportunity cost rate

nNumber of periods — years, months, or other time intervals

Present value formula

Formula

PV = \frac{FV}{(1 + r)^n}

Present value equals future value divided by the compound growth factor. This is the inverse of the future value formula. It answers: what is this future payment worth today, given a discount rate of r per period over n periods?

PVPresent value — what the future amount is worth today

FVFuture value — the amount to be received in the future

rDiscount rate per period — the opportunity cost or required rate of return

(1+r)^nThe discount factor — dividing by this converts future money to present money

Worked examples

Example 1Present value of a future payment

Given: You will receive 10.000 in 5 years. Discount rate: 6% per year.

Result: Present value today: 7.473

PV = 10.000 / (1,06)^5 = 10.000 / 1,3382 = 7.473. This means: receiving 10.000 in 5 years is equivalent to receiving 7.473 today, if you can invest at 6% per year. If someone offers to pay you 10.000 in 5 years or 8.000 today, you should take the 8.000 today, because 8.000 now is worth more than 7.473 (the present value of the future 10.000).

Example 2Comparing two payment options

Given: Option A: 50.000 today. Option B: 70.000 in 4 years. Discount rate: 8%.

Result: PV of Option B: 51.440. Take Option B.

PV of 70.000 in 4 years at 8%: PV = 70.000 / (1,08)^4 = 70.000 / 1,3605 = 51.440. Since 51.440 > 50.000, Option B is worth more in present value terms. Waiting 4 years for the extra 20.000 is justified because the present value of that future amount exceeds the immediate payment.

Example 3How long to double at given rate

Given: How many years to double 5.000 at 7% per year?

Result: Approximately 10,2 years

Solve for n in FV = PV x (1+r)^n when FV = 2 x PV: 2 = (1,07)^n. Taking logarithms: n = ln(2) / ln(1,07) = 0,693 / 0,0677 = 10,24 years. The Rule of 72 gives 72/7 = 10,3 years, which matches closely.

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TVM in loans, bonds and pension planning

The time value of money is embedded in every major financial product.

Loans: when a bank lends you 200.000, the total repayments over 25 years amount to far more than 200.000. Each future payment is discounted back to the present at the loan rate. The sum of all those present values equals exactly 200.000 — the current loan amount. This is why loan pricing is fundamentally a TVM problem.

Bonds: a bond pays a series of coupon payments and a final face value repayment. The price of the bond is the present value of all these future cash flows, discounted at the market yield. When yields rise, the discount rate rises and bond prices fall. When yields fall, bond prices rise. This inverse relationship is a direct consequence of the TVM formula.

Pension planning: the question 'how much must I save today to fund a specific retirement income?' is a TVM problem. You need to find the present value of all future pension payments, then determine how much investment today at a given return rate is needed to accumulate that amount by retirement age.

Common mistakes

✗ Comparing cash flows at different points in time without discounting to a common date

✓ You cannot directly compare 50.000 today to 70.000 in 4 years without converting both to the same point in time. Always discount all future cash flows to their present value before comparing them.

✗ Using the inflation rate as the discount rate for all TVM calculations

✓ The appropriate discount rate is the opportunity cost — the return you could earn on an alternative investment of equal risk. For low-risk decisions, use a risk-free rate. For business investment appraisal, use the company's weighted average cost of capital (WACC).

✗ Ignoring TVM when evaluating long-term financial decisions

✓ Paying 1.000 per year for 20 years is not the same as paying 20.000 today. The present value of the 20 payments (at 5% discount rate) is approximately 12.462 — significantly less than 20.000. Always account for TVM in any multi-period financial analysis.

Methodology

Future value uses FV = PV x (1+r)^n. Present value uses PV = FV / (1+r)^n. All examples use annual compounding and end-of-period cash flows unless otherwise stated. The discount rate represents the opportunity cost appropriate for the risk level of the cash flows being valued.

TVM calculations produce precise results given the assumed discount rate. The discount rate itself involves judgement and is the key variable in any valuation. Results are for educational illustration and do not constitute financial advice.

Cite this guide

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https://calquify.com/guides/time-value-of-money

Last updated: May 2026

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Frequently asked questions

What is the time value of money in simple terms?

Money today is worth more than the same amount in the future, because money today can be invested to earn a return. If you can earn 5% per year, 1.000 today grows to 1.050 in one year. So 1.000 promised in one year is worth only 952 today (the amount you could invest now to get 1.000 in one year). The difference of 48 is the time value — the cost of waiting one year to receive the money.

What discount rate should I use in TVM calculations?

The discount rate should reflect the opportunity cost — what you could earn on an alternative investment of comparable risk. For very safe cash flows, use a risk-free rate (government bond yield). For corporate cash flows, use the weighted average cost of capital (WACC). For personal financial decisions, use the rate you could earn on savings or investments of similar risk.

How does the time value of money affect loan interest?

Loan interest is the compensation a lender receives for providing money now rather than waiting. The interest rate reflects: the lender's opportunity cost (what they forgo by lending rather than investing), inflation expectations, and a risk premium for the possibility of default. The sum of all future loan repayments, discounted at the loan rate, equals exactly the original loan amount. This is why the loan pricing and amortization schedule are both TVM calculations.

What is the present value of receiving money forever (a perpetuity)?

A perpetuity is an infinite series of equal payments. Its present value is: PV = Payment / r, where r is the discount rate. If you receive 1.000 per year forever and the discount rate is 5%, the present value is 1.000 / 0,05 = 20.000. This formula is used to value stocks that pay a constant dividend indefinitely (Gordon Growth Model) and certain types of bonds.

Sources & References

› Investopedia — Time Value of Money Retrieved 2026-05-17

› CFA Institute — TVM in fixed income Retrieved 2026-05-17

Formula based on standard mathematical and financial methods. Results are for informational purposes. Last reviewed May 2026. Version 1.