{ I n v e s t m e n t s I n 2 0 0 7 , E ' T R A D E ...

\mathrm{\{} I n v e s t m e n t s ~ I n ~ 2 0 0 7 , ~ E ' T R A D E ~ F i n a n c i a l ~ w a s ~ o f f e r i n g ~ $4.94 \%$ interest on its online savings accounts, with interest reinvested monthly. ${ }^{19}$ Find the associated exponential model for the value of a $\$ 5,000$ deposit after $t$ years. Assuming this rate of return continued for seven years, how much would a deposit of $\$ 5,000$ at the beginning of 2007 be worth at the end of $2014 ?$ (Answer to the nearest \$1.) HINT [See Example 9 ; you saw this exercise before in Section 1.2.]

\mathrm{\{} I n v e s t m e n t s ~ I n ~ 2 0 0 7 , ~ E ' T R A D E ~ F i n a n c i a l ~ w a s ~ o f f e r i n g ~ $4.94 \%$
interest on its online savings accounts, with interest reinvested monthly. ${ }^{19}$ Find the associated exponential model for the value of a $\$ 5,000$ deposit after $t$ years. Assuming this rate of return continued for seven years, how much would a deposit of $\$ 5,000$ at the beginning of 2007 be worth at the end of $2014 ?$ (Answer to the nearest \$1.) HINT [See Example 9 ; you saw this exercise before in Section 1.2.]

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Key Concepts

Compound Interest

Compound interest is the process where interest is earned not only on the initial principal but also on the accumulated interest from previous periods. This concept is fundamental to understanding how investments grow over time, as each period’s interest calculation includes the previous gains, leading to exponential growth rather than mere linear accumulation.

Exponential Growth Model

The exponential growth model is used to represent situations where a quantity increases at a rate proportional to its current value. In financial contexts, this model describes how an investment grows over time with compound interest. The general formula, where a principal is multiplied by a growth factor raised to the power of time, captures the nature of investments appreciating at a constant periodic rate.

Compounding Frequency

Compounding frequency refers to the number of times interest is applied to an investment within a specific time period, such as monthly, quarterly, or annually. This concept is crucial because the frequency of compounding directly influences the effective rate of return; more frequent compounding results in faster accumulation of interest over time.

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