Question

An accountant uses the function \(R(v)=\frac{2000}{v+100}\) to predict the pattern of return of a particular investment, where \(R\) is the return, expressed as a percentage, and \(v\) is the dollar value invested. What return can she expect from an investment of \(\$ 400\) ? A. \(2 \%\) B. \(4 \%\) C. \(5 \%\) D. \(10 \%\)

Short answer

4%

Step-by-step solution

- Understand the given function

The given function is \( R(v) = \frac{2000}{v+100} \). It represents the return \(R\) as a percentage based on the dollar value invested \(v\).

- Identify the given investment value

The problem states that the investment value is \$400. So, \( v = 400 \).

- Substitute the investment value into the function

Replace \( v \) in the function with 400: \[ R(400) = \frac{2000}{400 + 100} \]

- Perform the arithmetic operations

Simplify the expression by first calculating the denominator: \[ 400 + 100 = 500 \] Now, substitute this back into the function: \[ R(400) = \frac{2000}{500} \]

- Calculate the final result

Divide 2000 by 500 to find the return: \[ R(400) = \frac{2000}{500} = 4 \] Therefore, the return on an investment of \$400 is 4\%. This corresponds to option B.

Key concepts

Investment Return Calculation

When it comes to evaluating investment performance, understanding how to calculate returns is crucial. Return on investment (ROI) helps investors assess the profitability of their investments. In our provided exercise, the accountant uses a function-based approach to predict returns. The formula given is: .Standardized formulas like this allow for easily converting investment values into percentage returns, helping forecast and compare investment opportunities effectively.

Function Evaluation

Function evaluation involves substituting a given input value into a function to obtain an output value. In the context of the exercise, the function is: . Here, the input value is the dollar amount invested ( ) and the output value is the investment return ( . . To evaluate this function for an investment of ) $ . Applying these principles ensures accurate predictions for different investment amounts.

Arithmetic Operations

Mastery of basic arithmetic operations is essential when calculating investment returns. The exercise demonstrates several arithmetic steps:

• Addition: To combine the investment value with 100 ( ) creates the denominator of the fraction.
• Division: Dividing 2000 by the resulting sum to obtain the return percentage.

Simplifying expressions systematically helps ensure accuracy and clarity in calculations. It's fundamental to break down each arithmetic operation step by step as shown.

Step-by-Step Solution

Approaching problems with a step-by-step method can drastically improve comprehension and accuracy. Our exercise can be broken down into distinct steps:
Identify the function and its components ( ).
Recognize the given input value (investment amount).
Substitute the input value into the function and simplify the resulting expression by performing arithmetic operations stepwise.
Calculate the final result to determine the investment return.
Present each step clearly and logically to solve problems effectively and ensure they can be easily followed and understood by students.