Question
You have $12,000 to invest in a stock that promises 4.5% growth annually.
A. Write an algebraic function that represents the scenario.
B. Determine the total amount in your account at 4,8, and 10 years.
A. Write an algebraic function that represents the scenario.
B. Determine the total amount in your account at 4,8, and 10 years.
Answers
GPT 3.5
A. Let A(t) represent the total amount in your account after t years with an initial investment of $12,000 and 4.5% growth annually. The formula for compound interest is:
A(t) = 12000(1 + 0.045)^t
B.
For t = 4 years:
A(4) = 12000(1 + 0.045)^4
A(4) = 12000(1.045)^4
A(4) = 12000(1.193663166)
A(4) = $14,323.96
For t = 8 years:
A(8) = 12000(1 + 0.045)^8
A(8) = 12000(1.045)^8
A(8) = 12000(1.222161217)
A(8) = $14,665.94
For t = 10 years:
A(10) = 12000(1 + 0.045)^10
A(10) = 12000(1.045)^10
A(10) = 12000(1.280084544)
A(10) = $15,361.01
A(t) = 12000(1 + 0.045)^t
B.
For t = 4 years:
A(4) = 12000(1 + 0.045)^4
A(4) = 12000(1.045)^4
A(4) = 12000(1.193663166)
A(4) = $14,323.96
For t = 8 years:
A(8) = 12000(1 + 0.045)^8
A(8) = 12000(1.045)^8
A(8) = 12000(1.222161217)
A(8) = $14,665.94
For t = 10 years:
A(10) = 12000(1 + 0.045)^10
A(10) = 12000(1.045)^10
A(10) = 12000(1.280084544)
A(10) = $15,361.01