Compound Interest Which of the given interest rates and...

Compound Interest Which of the given interest rates and compounding periods would provide the better investment?
(a) 5$\%$ per year, compounded semiannully
(b) 5$\%$ per year, compounded continuously

Key Concepts

Continuous Compounding

Continuous compounding is the limit where the compounding period is infinitesimally small, essentially applying interest at every moment. It is mathematically modeled using the exponential function, resulting in a slightly higher effective rate than conventional periodic compounding when an identical nominal interest rate is used.

Semiannual Compounding

Semiannual compounding refers to interest being compounded twice a year. In each of these periods, interest is calculated on the accumulated amount, and then it is added to the principal for the next period, leading to a higher amount of compounded interest over time compared to less frequent compounding.

Compound Interest

Compound interest is the process in which interest earned on an investment is reinvested to earn additional interest, resulting in exponential growth over time. Unlike simple interest, where interest is calculated solely on the original principal, compound interest takes into account accumulated interest from previous periods.

Effective Annual Rate

The effective annual rate (EAR) is a calculation that adjusts the nominal interest rate to account for the effects of compounding within a year. It provides a standardized measure to compare different interest rates with varying compounding frequencies by reflecting the actual annual return on an investment.

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