In 2007 , ING Direct was offering 4.14 % interest on its...

In 2007 , ING Direct was offering $4.14 \%$ interest on its online Orange Savings Account, with interest reinvested quarterly. $^{26}$ Find the associated exponential model for the value of a $\$ 4,000$ deposit after $t$ years. Assuming this rate of return continued for eight years, how much would a deposit of $\$ 4,000$ at the beginning of 2007 be worth at the start of 2015 ? (Answer to the nearest \$1.)

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Key Concepts

Exponential Growth

This concept refers to processes where the rate of change (growth or decay) of a quantity is proportional to its current value. In financial contexts, it models how investments or loans increase over time when interest is applied, leading to a growth pattern that can be represented using exponential functions.

Compound Interest

Compound interest involves calculating interest on both the initial principal and the accumulated interest from previous periods. This method of interest accounting leads to exponential growth in the value of an investment, distinguishing it from simple interest, where interest is computed solely on the principal amount.

Periodic Compounding

Periodic compounding is a specific application of compound interest where interest is added at regular intervals, such as monthly, quarterly, or annually. This concept highlights the importance of dividing the annual nominal interest rate by the number of compounding periods and then raising the growth factor to the power of the total number of periods over the life of the investment.

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