Suppose you deposit $2000 in a savings account that pays interest at an annual rate of 4%. If no money is added or withdrawn from the account, answer the following questions.
A. 4 years
B. 6 years
A. After 4 years, the amount in the savings account can be calculated using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, P = $2000, r = 0.04 (4% annual interest rate), n = 1 (compounded annually), and t = 4 (4 years). Plugging these values into the formula:
A = 2000(1 + 0.04/1)^(1*4)
A = 2000(1.04)^4
A = 2000(1.16986)
A = $2339.73
Therefore, after 4 years, the amount in the savings account will be approximately $2339.73.
B. After 6 years, using the same formula:
A = 2000(1 + 0.04/1)^(1*6)
A = 2000(1.04)^6
A = 2000(1.259712)
A = $2519.42
Therefore, after 6 years, the amount in the savings account will be approximately $2519.42.