Question

2 leonard purchased 6910 shares of stock at $27.95 per share. he sold the stock 3 years later at $53.36 per share. what is leon’s approximate capital gains percentage to the nearest percent? \\(\frac{(\text{current price} \times \text{# of shares}) - (\text{initial price} \times \text{# of shares})}{(\text{initial price} \times \text{# of shares})}\\) \\(\boldsymbol{\text{a}}\\) 85% \\(\boldsymbol{\text{b}}\\) 81% \\(\boldsymbol{\text{c}}\\) 91% \\(\boldsymbol{\text{d}}\\) 95%

Explanation:

Step1: Simplify the formula

Notice that the number of shares (6910) is a common factor in the numerator and denominator, so we can simplify the capital gains percentage formula. The formula \(\frac{(\text{current price} \times \# \text{ of shares}) - (\text{initial price} \times \# \text{ of shares})}{(\text{initial price} \times \# \text{ of shares})}\) can be factored as \(\frac{\# \text{ of shares} \times (\text{current price} - \text{initial price})}{\# \text{ of shares} \times \text{initial price}}\), and the \(\# \text{ of shares}\) terms cancel out, leaving \(\frac{\text{current price} - \text{initial price}}{\text{initial price}}\).

Step2: Substitute the values

The initial price per share is \(\$27.95\) and the current price per share is \(\$53.36\). Substitute these values into the simplified formula: \(\frac{53.36 - 27.95}{27.95}\).

Step3: Calculate the numerator

First, calculate the numerator: \(53.36 - 27.95 = 25.41\).

Step4: Calculate the fraction

Now, divide the numerator by the denominator: \(\frac{25.41}{27.95} \approx 0.909\).

Step5: Convert to a percentage

To convert this decimal to a percentage, multiply by 100: \(0.909 \times 100 \approx 91\%\) (rounded to the nearest percent).

Answer:

C. 91%