- Calculate the total initial investment: \(300 \times \$16.99 = \$5,097.00\).
- Establish the profit equation: \(\$5,000.00 = (300 \times x) - \$5,097.00\), where \(x\) is the required NAV.
- Solve for \(x\): \(x = \frac{\$10,097.00}{300} \approx \$33.6567\).
- Select the closest value from the provided options, which is \(\boxed{\$33.66}\).
Explanation
- Analysis of Investment and Profit Calculation
Nezzie is investing in 300 shares of the 'LKIT Mid-Cap' fund at an offer price of \(\$16.99\) per share. To determine the total initial cost of her investment, we multiply the number of shares by the offer price per share:
\[\text{Total Cost} = 300 \times \$16.99 = \$5,097.00\]
Nezzie plans to sell her shares when she achieves a total profit of \(\$5,000.00\). Profit is calculated as the difference between the total proceeds from the sale and the total cost of the initial investment. Let \(x\) be the Net Asset Value (NAV) per share at the time of sale. The total proceeds from the sale of 300 shares will be \(300 \times x\). Thus, the equation for her profit is:
\[\text{Profit} = (\text{Total Proceeds}) - (\text{Total Cost})\]
\[\$5,000.00 = (300 \times x) - \$5,097.00\]
- Solving for the Net Asset Value
To find the NAV (\(x\)) required to reach the target profit, we isolate \(x\) in the profit equation:
\[\$5,000.00 + \$5,097.00 = 300 \times x\]
\[\$10,097.00 = 300 \times x\]
Dividing both sides by 300 gives:
\[x = \frac{\$10,097.00}{300} \approx \$33.6567\]
Comparing this result to the given options:
A\(\$16.67\)
B\(\$33.25\)
C\(\$33.57\)
D\(\$33.66\)
The value \(\$33.6567\) is closest to \(\$33.66\), which is option (d).
- Conclusion
By rounding our calculated value to the nearest cent, we determine that the NAV must be approximately \(\$33.66\) for Nezzie to meet her target profit goal of \(\$5,000.00\). Therefore, the correct option is (d). The final answer is \(\boxed{\$33.66}\).
Examples
In personal finance, calculating the necessary asset value to reach a target profit is a crucial skill for investors. Whether managing mutual fund shares, stocks, or real estate, knowing the 'break-even' point or the target selling price helps in setting realistic goals. For example, if you bought a collection of vintage items for \(\$2,000\) and aim to make a \(\$500\) profit, you would use a similar calculation to determine that you must sell the items for a total of \(\$2,500\). Applying these algebraic techniques allows for precise financial planning and better decision-making in any market.