When Interest Is Compounded Continuously, the Rate of Change of the Amount

question 49

Multiple Choice

When interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. In this case, the proportionality constant is the annual interest rate r (as a decimal) ; that is, . If $2,500 is invested at 7%, compounded continuously, what will be the future value of this investment after 12 years? Round to the nearest cent. ​

• A)$4,600.00
• B)$5,776.80
• C)$5,630.48
• D)$5,708.32
• E)$5,790.92

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Definitions:

Six-Stage Process

Typically refers to a structured sequence of steps designed to complete a task or solve a problem, often used in project management, therapy, or conflict resolution.

Contemplation Stage

A phase in the process of change where an individual is aware a change is needed and actively thinking about making it, but has not yet committed to action.

Action Stage

A phase in the process of change where individuals actively implement behaviors to achieve a desired outcome.

Affective Discrepancy

A psychological term referring to a gap or difference between felt emotions and expressed emotions.