If P Dollars Are Invested at an Annual Rate of R

question 37

Multiple Choice

If P dollars are invested at an annual rate of r%, then in t years this investment grows to F dollars, where $F = P \left( 1 + \frac { r } { 100 } \right) ^ { t }$ .Assuming P and r are constant, find $\frac { d F } { d t }$ .

• A) \(P \left( 1 + \frac { r } { 100 } \right) ^ { t }\)
• B) \(P t \left( 1 + \frac { r } { 100 } \right) ^ { t - 1 }\)
• C) \(P \left( 1 + \frac { r } { 100 } \right) ^ { t } \ln \left( 1 + \frac { r } { 100 } \right)\)
• D) \(\frac { P \left( 1 + \frac { r } { 100 } \right) ^ { t } } { \ln \left( 1 + \frac { r } { 100 } \right) }\)

---

Definitions:

Creative Destruction

An economic theory that suggests the dismantling of long-standing practices in order to make way for innovation and new systems that enhance economic vitality.

Joseph Schumpeter

An economist and political scientist who proposed the theory of creative destruction in economics.

New Businesses

New businesses are entities in their early stages of operation, often characterized by innovation, development of products or services, and efforts to secure market position.

Small Business Characteristics

Pertains to features that define small businesses, such as limited revenue and workforce size, often centered around personalized service and local operation.