You want to invest 5000 in a certificate of deposit for 12...

You want to invest $\$ 5000$ in a certificate of deposit for 12 months. You are given the options below. Which would you choose? Explain.
(a) $r=5.25 \%$, quarterly compounding
(b) $r=5 \%,$ monthly compounding
(c) $r=4.75 \%$, continuous compounding

Key Concepts

Compound Interest

Compound interest is the process where interest is added to the principal so that, from that moment on, the interest that has been added also earns interest. This fundamental concept in finance leads to exponential growth of the investment over time and is used when the accumulation of interest occurs at regular intervals.

Compounding Frequency

Compounding frequency refers to how often the accrued interest is added to the principal, which in turn affects how quickly the investment grows. More frequent compounding results in faster accumulation of interest, highlighting the importance of understanding timing and intervals in financial calculations.

Effective Annual Rate (EAR)

The Effective Annual Rate (EAR) is the actual annual rate of interest earned or paid on an investment or loan after accounting for compounding effects over the year. It allows for a true comparison of different financial products that have varying compounding intervals.

Continuous Compounding

Continuous compounding is an idealized limit where interest is calculated and added to the account balance an infinite number of times per year. It uses the exponential function to model growth, typically yielding slightly higher returns compared to discrete compounding methods over the same nominal rate.

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