Question
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 in 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?
Answers
GPT 3.5
First, let's calculate how much money was invested in stocks and how much was left in the savings account:
Amount invested in stocks = $5,000 x 60% = $3,000
Amount left in savings account = $5,000 - $3,000 = $2,000
In the first year, the stock increases by 9%, so the value of the stock investment after the first year is:
$3,000 + ($3,000 x 9%) = $3,000 + $270 = $3,270
In the second year, the stock loses 4% of its value, so the final value of the stock investment after the second year is:
$3,270 - ($3,270 x 4%) = $3,270 - $130.80 = $3,139.20
Now, let's calculate the total amount gained from the stock investment over the 2 years:
Total gain from stocks = $3,139.20 - $3,000 = $139.20
Next, let's calculate the total amount gained if the entire $5,000 had been left in the savings account at an APR of 4.9% for 2 years:
Total amount gained from savings account = $5,000 x 4.9% x 2 = $5000 x 0.049 x 2 = $490
Therefore, the total amount gained during the 2 years from the investment in stocks and the savings account is $139.20 + $490 = $629.20.
Amount invested in stocks = $5,000 x 60% = $3,000
Amount left in savings account = $5,000 - $3,000 = $2,000
In the first year, the stock increases by 9%, so the value of the stock investment after the first year is:
$3,000 + ($3,000 x 9%) = $3,000 + $270 = $3,270
In the second year, the stock loses 4% of its value, so the final value of the stock investment after the second year is:
$3,270 - ($3,270 x 4%) = $3,270 - $130.80 = $3,139.20
Now, let's calculate the total amount gained from the stock investment over the 2 years:
Total gain from stocks = $3,139.20 - $3,000 = $139.20
Next, let's calculate the total amount gained if the entire $5,000 had been left in the savings account at an APR of 4.9% for 2 years:
Total amount gained from savings account = $5,000 x 4.9% x 2 = $5000 x 0.049 x 2 = $490
Therefore, the total amount gained during the 2 years from the investment in stocks and the savings account is $139.20 + $490 = $629.20.