Question
Shota invests
\[\$1000\] in a certificate of deposit that earns interest. The investment's value is multiplied by
\[1.02\] each year.
Which expression gives the investment's value after
\[5\] years?
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[1000\cdot 1.02^5\]
A
\[1000\cdot 1.02^5\]
(Choice B)
\[1000+(1+1.02)^5\]
B
\[1000+(1+1.02)^5\]
(Choice C)
\[1000+ 1.02^5\]
C
\[1000+ 1.02^5\]
(Choice D)
\[1000\cdot (1+1.02)^5\]
D
\[1000\cdot (1+1.02)^5\]
\[\$1000\] in a certificate of deposit that earns interest. The investment's value is multiplied by
\[1.02\] each year.
Which expression gives the investment's value after
\[5\] years?
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[1000\cdot 1.02^5\]
A
\[1000\cdot 1.02^5\]
(Choice B)
\[1000+(1+1.02)^5\]
B
\[1000+(1+1.02)^5\]
(Choice C)
\[1000+ 1.02^5\]
C
\[1000+ 1.02^5\]
(Choice D)
\[1000\cdot (1+1.02)^5\]
D
\[1000\cdot (1+1.02)^5\]
Answers
GPT-4o mini
To determine the investment's value after 5 years, we can recognize that the investment's value is multiplied by 1.02 each year. Therefore, the formula to calculate the value after \( n \) years with an initial investment \( P \) is:
\[
P \cdot (1 + r)^n
\]
Where \( r \) is the interest rate (in this case, \( 0.02 \)), and \( n \) is the number of years. In this scenario:
- \( P = 1000 \)
- \( r = 0.02 \)
- \( n = 5 \)
Therefore, the value of the investment after 5 years can be expressed as:
\[
1000 \cdot (1.02)^5
\]
This matches with Choice A:
\[
1000 \cdot 1.02^5
\]
Thus, the correct answer is:
**(Choice A) \( 1000\cdot 1.02^5 \)**
\[
P \cdot (1 + r)^n
\]
Where \( r \) is the interest rate (in this case, \( 0.02 \)), and \( n \) is the number of years. In this scenario:
- \( P = 1000 \)
- \( r = 0.02 \)
- \( n = 5 \)
Therefore, the value of the investment after 5 years can be expressed as:
\[
1000 \cdot (1.02)^5
\]
This matches with Choice A:
\[
1000 \cdot 1.02^5
\]
Thus, the correct answer is:
**(Choice A) \( 1000\cdot 1.02^5 \)**