For questions 19–20, you will be answering WorkPad questions (6 points each – 2 points for the correct answers and 4 points for a correct explanation of your process).
You save $5,000.00 and invest 60% of it in stocks while leaving the rest in a savings account earning a 4.9% APR. The stock increases 9% in the first year and loses 4% of its value the second year. What is the total amount gained during the 2 years? What would the gain have been if all of the investment had been left in the savings account?
Be sure to include in your response:
the answer to the original question
the mathematical steps for solving the problem demonstrating mathematical reasoning
First, let's calculate the total amount gained from investing $5,000.00.
Step 1: Calculate the amount invested in stocks
60% of $5,000.00 = 0.60 * $5,000.00 = $3,000.00
Step 2: Calculate the amount left in the savings account
40% of $5,000.00 = 0.40 * $5,000.00 = $2,000.00
Step 3: Calculate the stock value after the first year
$3,000.00 * 1.09 = $3,270.00
Step 4: Calculate the stock value after the second year
$3,270.00 * 0.96 = $3,139.20
Step 5: Calculate the total amount gained from investing in stocks
$3,139.20 - $3,000.00 = $139.20
Now, let's calculate the total amount gained if all of the investment was left in the savings account earning a 4.9% APR.
Step 1: Calculate the total amount after the first year in the savings account
$2,000.00 * 1.049 = $2,098.00
Step 2: Calculate the total amount after the second year in the savings account
$2,098.00 * 1.049 = $2,202.80
Step 3: Calculate the total amount gained in the savings account
$2,202.80 - $2,000.00 = $202.80
Therefore, the total amount gained during the 2 years by dividing the investment between stocks and the savings account is $139.20. If all of the investment had been left in the savings account, the gain would have been $202.80.