What the formula calculates
Compound interest calculates the future value A of a principal P after t years at an annual interest rate r compounded n times per year. The formula is A = P(1 + r/n)^(nt). Unlike simple interest, which applies only to the original principal, compound interest applies to both the principal and all previously accumulated interest.
Compounding frequencies
The compounding frequency n determines how often interest is added to the principal. Annual compounding (n=1) applies interest once a year. Monthly compounding (n=12) applies interest twelve times a year, producing slightly higher returns. Daily compounding (n=365) is common in high-yield savings accounts and maximises the compounding effect.
Worked example
A principal of $10,000 invested at 7% annual interest compounded monthly for 10 years: A = 10000 × (1 + 0.07/12)^(12×10) = 10000 × (1.005833)^120 ≈ $20,097. The account more than doubles due to compounding.
The rule of 72
A quick mental approximation: divide 72 by the annual interest rate to estimate how many years it takes for an investment to double. At 7% annual return, 72/7 ≈ 10.3 years. At 10%, 72/10 = 7.2 years. This approximation works well for rates between 4% and 20%.