Compound Interest Fundamentals

Summary

Compound interest is interest earned on both an original principal amount and the interest accumulated in previous periods. Unlike simple interest, which is calculated only on the initial principal, compound interest grows through the reinvestment or retention of interest. The final amount depends on the principal, annual interest rate, investment duration, and compounding frequency, which may be annual, semiannual, quarterly, monthly, daily, or continuous. For periodic compounding, the accumulated amount is calculated using A = P(1 + r/n)^(nt), where P is the principal, r is the nominal annual interest rate, n is the number of compounding periods per year, and t is the time in years. More frequent compounding generally produces a higher effective annual return. With continuous compounding, the formula becomes A = Pe^(rt), and the effective annual rate approaches e^r - 1. Compound interest principles also apply to investments with recurring deposits, loans, mortgages, and the conversion of rates between different compounding bases.

Key Points

• 1

  Compound interest is calculated on the original principal plus previously accumulated interest, causing growth to accelerate over time.

• 2

  The periodic compounding formula is A = P(1 + r/n)^(nt), where compounding frequency significantly affects the final accumulated amount.

• 3

  The effective annual rate allows financial products with different compounding frequencies to be compared on a consistent yearly basis.

• 4

  Continuous compounding is modeled by A = Pe^(rt), with the continuous rate related to a periodic rate by δ = ln(1 + r).

• 5

  Recurring deposits can be valued using geometric-series formulas that account for the different lengths of time each deposit earns interest.