Compound Interest Calculator

What is compound interest?

Compound interest is one of the most powerful financial concepts, often called the "eighth wonder of the world" by Albert Einstein. Unlike simple interest where interest is calculated only on the initial principal, compound interest is calculated on the principal plus all previously accrued interest. This leads to exponential growth over time, significantly exceeding results from simple interest.

Compound interest formula

The compound interest formula is A = P(1 + r/n)^(nt), where P is the 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. For continuous compounding the formula simplifies to A = Pe^(rt). This formula helps calculate the future value of an investment at different compounding frequencies.

Rule of 72

The Rule of 72 is a quick method to estimate the time needed to double an investment at a given rate of return. Simply divide 72 by the annual interest rate. At 8% per year, the investment doubles in about 9 years (72 ÷ 8 = 9). This simple formula is extremely useful for quick financial planning and illustrating compound interest's power.

Practical applications

• Savings and bank deposits
• Stock investments (reinvested dividends)
• Pension and investment funds
• Loans and credit (interest on interest)

Compounding frequency affects growth

Compounding frequency significantly affects the final investment value. More frequent compounding yields greater compounding effect. The difference between annual and monthly compounding with 1000 PLN at 10% for 10 years is about 150 PLN. With longer periods and higher rates, the difference grows significantly. This should be considered when choosing financial products.