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Math  /  Numbers & Operations

QuestionCompute the total and annual returns on the described investment. Six years after buying 50 shares of XYZX Y Z stock for $80\$ 80 per share, you sell the stock for $5600\$ 5600.
The total return is □\square \%. (Do not round until the final answer. Then round to one decimal place as needed.)

Studdy Solution

STEP 1

1. You initially bought 50 shares of stock at \$80 per share.
2. You sold the stock for a total of \$5600 after six years.
3. Total return is calculated as the percentage increase from the initial investment.
4. Annual return is calculated using the compound annual growth rate (CAGR) formula.

STEP 2

1. Calculate the initial investment.
2. Calculate the total return.
3. Calculate the annual return.

STEP 3

Calculate the initial investment by multiplying the number of shares by the purchase price per share.
Initial Investment = Number of Shares ×\times Purchase Price per Share
50×80=4000 50 \times 80 = 4000

STEP 4

Calculate the total return using the formula:
Total Return=(Final Value−Initial InvestmentInitial Investment)×100\text{Total Return} = \left(\frac{\text{Final Value} - \text{Initial Investment}}{\text{Initial Investment}}\right) \times 100
Substitute the given values:
Total Return=(5600−40004000)×100\text{Total Return} = \left(\frac{5600 - 4000}{4000}\right) \times 100

STEP 5

Simplify the expression to find the total return.
Total Return=(16004000)×100=0.4×100=40%\text{Total Return} = \left(\frac{1600}{4000}\right) \times 100 = 0.4 \times 100 = 40\%

STEP 6

Calculate the annual return using the compound annual growth rate (CAGR) formula:
CAGR=(Final ValueInitial Investment)1n−1\text{CAGR} = \left(\frac{\text{Final Value}}{\text{Initial Investment}}\right)^{\frac{1}{n}} - 1
where n n is the number of years.
Substitute the given values:
CAGR=(56004000)16−1\text{CAGR} = \left(\frac{5600}{4000}\right)^{\frac{1}{6}} - 1

STEP 7

Simplify the expression to find the annual return.
CAGR=(1.4)16−1\text{CAGR} = \left(1.4\right)^{\frac{1}{6}} - 1
Calculate the value:
CAGR≈1.0583−1=0.0583\text{CAGR} \approx 1.0583 - 1 = 0.0583
Convert to percentage:
Annual Return≈5.8%\text{Annual Return} \approx 5.8\%
The total return is 40%\boxed{40\%} and the annual return is approximately 5.8%\boxed{5.8\%}.

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