Compound Interest Calculator

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Because each period's interest is added to the balance, the effective rate grows over time, leading to exponential rather than linear growth.

The basic formula is FV = PV × (1 + r/n)^(n×t), where PV is the present value (initial principal), r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years. Example: 10 000 × (1.08)^10 ≈ 21 589.

The Rule of 72 estimates how many years it takes to double your money: divide 72 by the annual interest rate. At 8% per year: 72/8 = 9 years. It is an approximation — the exact answer is ln(2)/ln(1.08) ≈ 9.01 years.

Yes — more frequent compounding yields a higher final balance. At 8% on 10 000 PLN over 10 years: annual compounding gives ~21 589, monthly compounding gives ~22 197. The difference increases with higher rates and longer periods.

Regular contributions significantly accelerate growth through the same compounding effect. Each payment starts earning interest immediately. The earlier contributions begin, the larger the long-term impact. Even small monthly amounts can meaningfully increase final capital.

Albert Einstein reportedly called compound interest the 'eighth wonder of the world'. The long-term exponential growth effect means even modest savings can grow into substantial sums. 10 000 PLN at 8% annually grows to over 100 000 PLN in 30 years.

Simple interest is calculated only on the original principal: gain = PV × r × t. Compound interest adds each period's gain to the balance. Example: 1 000 PLN, 10%, 3 years — simple: 300 PLN gain; compound (annual): 331 PLN gain.

CAGR is the annual rate at which an investment would grow from its starting value to its ending value, assuming reinvestment of gains each year. Formula: CAGR = (FV/PV)^(1/t) − 1. It is the standard metric for comparing investment performance across different time periods.

The nominal rate does not account for inflation. Real rate ≈ (1 + nominal) / (1 + inflation) − 1. If you earn 8% nominally and inflation is 3%, the real rate is about 4.85%. Always compare your expected return against the current inflation rate.

A bank deposit has a fixed, guaranteed interest rate. An ETF tracks a basket of stocks or bonds — historical returns are potentially higher (S&P 500: ~10% annually in nominal terms) but variable and not guaranteed. In both cases compound growth applies, but ETF returns fluctuate year to year.