An investor will use $2{,}000 to purchase 10 shares of a certain stock at $200 per share. At the same...
GMAT Two Part Analysis : (TPA) Questions
An investor will use \(\$2{,}000\) to purchase \(10\) shares of a certain stock at \(\$200\) per share. At the same time, she will invest another sum of money in a certificate of deposit (CD) that earns \(2\%\) simple interest annually. The investor would like to know how much money she should invest in the CD to meet her goal of net earnings (before any taxes or other fees) of \(\$360\) from the two investments at the end of one year.
In the table, select for CD assuming \(10\%\) gain the amount the investor should invest in the CD to meet her goal under the assumption that the stock price will have increased by \(10\%\) at the end of one year, and select for CD assuming \(5\%\) loss the amount she should invest in the CD to meet her goal under the assumption that the stock price will have decreased by \(5\%\) at the end of one year. Make only two selections, one in each column.
Let's visualize this problem to make it crystal clear...
Phase 1: Owning the Dataset
Visual Representation
Let's create a simple investment flow diagram:
Initial Investment → After 1 Year → Earnings Stock: $2,000 → Stock Value → Stock Gain/Loss CD: X amount → X + (X × 0.02) → CD Interest Target: Total Earnings = $360
Given Information
- Stock purchase: \(\mathrm{10\,shares \times \$200/share = \$2,000}\)
- CD interest rate: 2% simple interest annually
- Goal: Total net earnings = $360 after one year
- Two scenarios to consider:
- Stock increases by 10%
- Stock decreases by 5%
Phase 2: Understanding the Question
We need to find how much to invest in the CD for each scenario such that:
\(\mathrm{Stock\,Earnings + CD\,Interest = \$360}\)
Where:
- Stock Earnings = \(\mathrm{Final\,Stock\,Value - \$2,000}\)
- CD Interest = \(\mathrm{CD\,Investment \times 0.02}\)
Phase 3: Finding the Answer
Scenario 1: Stock Increases by 10%
Step 1: Calculate stock performance
- Initial stock value: $2,000
- After 10% increase: \(\mathrm{\$2,000 \times 1.10 = \$2,200}\)
- Stock earnings: \(\mathrm{\$2,200 - \$2,000 = \$200}\)
Step 2: Calculate required CD earnings
- Total earnings needed: $360
- Earnings from stock: $200
- Required from CD: \(\mathrm{\$360 - \$200 = \$160}\)
Step 3: Calculate CD investment amount
- CD Interest = \(\mathrm{CD\,Investment \times 0.02}\)
- \(\mathrm{\$160 = CD\,Investment \times 0.02}\)
- CD Investment = \(\mathrm{\$160 ÷ 0.02 = \$8,000}\)
Scenario 2: Stock Decreases by 5%
Step 1: Calculate stock performance
- Initial stock value: $2,000
- After 5% decrease: \(\mathrm{\$2,000 \times 0.95 = \$1,900}\)
- Stock earnings: \(\mathrm{\$1,900 - \$2,000 = -\$100}\) (loss)
Step 2: Calculate required CD earnings
- Total earnings needed: $360
- Earnings from stock: -$100
- Required from CD: \(\mathrm{\$360 - (-\$100) = \$460}\)
Step 3: Calculate CD investment amount
- CD Interest = \(\mathrm{CD\,Investment \times 0.02}\)
- \(\mathrm{\$460 = CD\,Investment \times 0.02}\)
- CD Investment = \(\mathrm{\$460 ÷ 0.02 = \$23,000}\)
Phase 4: Solution
Final Answer:
- CD assuming 10% gain: $8,000
- CD assuming 5% loss: $23,000