Future value: what a lump sum grows to with compound interest
Every euro invested today grows into a different amount tomorrow, and understanding that difference is the foundation of saving and investing. A future value calculator projects how an initial amount grows over time with a fixed interest rate, showing the power of compound interest on a single lump sum. It answers questions like "how much will my €10,000 be worth in 20 years?" with a single calculation.
TL;DR
- Future value applies compound interest: each period, the accumulated balance earns interest on both the original principal and the interest already earned.
- Formula: FV = PV × (1 + r)^n | with r = rate per period, n = number of periods
- Example 1: €10,000 at 5% for 20 years — Growth factor: (1 + 0.05) = 1.05
How it works
Future value applies compound interest: each period, the accumulated balance earns interest on both the original principal and the interest already earned. The growth is exponential, not linear, which is why long horizons dramatically amplify returns. The calculator compounds annually, monthly, or at any chosen frequency depending on the input.
The math
The future value formula raises the growth factor (1 + rate) to the power of the number of periods, then multiplies by the present value. When compounding is monthly, the annual rate is divided by 12 and the years are multiplied by 12 before applying the exponent.
This is the famous compound interest formula at the heart of every savings projection, from retirement funds to bond valuations.
Examples
Example 1: €10,000 at 5% for 20 years
- Growth factor: (1 + 0.05) = 1.05
- Raise to the 20th power: 1.05^20 ≈ 2.6533
- FV = €10,000 × 2.6533 = €26,533
- The money more than doubles despite "only" 5% yearly
Example 2: Monthly compounding at 6% for 10 years
- Monthly rate: 0.06 ÷ 12 = 0.005
- Periods: 10 × 12 = 120
- Factor: (1.005)^120 ≈ 1.8194
- FV = €10,000 × 1.8194 = €18,194
When to use it
✦ Savings and Investment Planning
Investors compare how different rates and horizons grow their lump sums, informing decisions between bonds, deposits, and equity funds.
✦ Education and Retirement Goals
Parents project how much a gift or inheritance will be worth by the time a child reaches university, and savers estimate retirement capital growth.
⚠ Common mistakes
- Confusing Nominal and Effective Rates: The effective annual rate is higher with frequent compounding; using the nominal rate understates growth.
- Ignoring Inflation: A future value in nominal euros overstates purchasing power; subtract inflation for a real-terms comparison.
- Forgetting Taxes and Fees: Real-world returns are reduced by management fees and capital gains taxes that formulas ignore.
FAQ (2)
What is the Rule of 72?
Divide 72 by the annual rate to approximate the years needed to double your money; at 6%, money doubles in about 12 years.
Does compounding frequency matter?
Yes, but modestly: monthly compounding beats annual compounding, and the advantage grows with the rate and the horizon.
Sources & References
⚠ Financial Disclaimer
This tool provides estimates for informational purposes only and does not constitute financial, tax, or legal advice. Results may vary based on local regulations, rates, and individual circumstances. Always consult a qualified professional before making financial decisions.