explain anwser
You invest $2,000.00 in a stock plan and another $2,000.00 in a savings account. The stock plan decreases by 7% the first year and gains 10% the second year. The savings account earns a 3.7% APR and compounds annually. What is the difference in earnings between the stock and savings account at the end of the second year?
Anwser is: 104.74
To calculate the earnings from the stock plan after two years:
First, calculate the stock's value after the first year:
$2,000.00 - (7% of $2,000.00) = $2,000.00 - $140 = $1,860.00
Then, calculate the stock's value after the second year:
$1,860.00 + (10% of $1,860.00) = $1,860.00 + $186.00 = $2,046.00
To calculate the earnings from the savings account after two years:
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (initial amount)
r = annual interest rate (3.7% or 0.037)
n = number of times interest is compounded per year (1, as it compounds annually)
t = number of years the money is invested for (2 years)
Plug in the values:
A = $2,000.00(1 + 0.037/1)^(1*2)
A = $2,000.00(1.037)^2
A = $2,000.00(1.074569)
A = $2,149.14
Subtract the initial investment from the final savings account value to find the earnings:
$2,149.14 - $2,000.00 = $149.14
Finally, calculate the difference in earnings between the stock plan and savings account at the end of the second year:
$2,149.14 - $2,046.00 = $104.74
Therefore, the difference in earnings between the stock and savings account at the end of the second year is $104.74.