Question
Daniel opens a new savings account and makes an initial deposit of $1,200. If the account earns 2.5% annual interest, which equation shows how much money is in the account in 9 months?
Responses
x=1,200+1,200(0.025)(9)
x=1,200+1,200(0.25)(9)
x=1,200+1,200(0.025)(0.75)
x=1,200+1,200(0.25)(0.75)
Responses
x=1,200+1,200(0.025)(9)
x=1,200+1,200(0.25)(9)
x=1,200+1,200(0.025)(0.75)
x=1,200+1,200(0.25)(0.75)
Answers
GPT-4o mini
To find out how much money is in the account after 9 months with an interest rate of 2.5%, we can use the formula for simple interest:
\[ A = P + P \times r \times t \]
where:
- \( A \) is the total amount of money in the account after interest,
- \( P \) is the principal amount (initial deposit),
- \( r \) is the annual interest rate (in decimal form),
- \( t \) is the time in years.
1. The principal amount \( P \) is $1,200.
2. The annual interest rate \( r \) is 2.5%, which is \( 0.025 \) in decimal form.
3. The time \( t \) is 9 months, which is \( \frac{9}{12} = 0.75 \) years.
Now we can set up the equation:
\[
A = 1,200 + 1,200 \times 0.025 \times 0.75
\]
Therefore, the correct choice that represents this equation is:
\[
x = 1,200 + 1,200(0.025)(0.75)
\]
\[ A = P + P \times r \times t \]
where:
- \( A \) is the total amount of money in the account after interest,
- \( P \) is the principal amount (initial deposit),
- \( r \) is the annual interest rate (in decimal form),
- \( t \) is the time in years.
1. The principal amount \( P \) is $1,200.
2. The annual interest rate \( r \) is 2.5%, which is \( 0.025 \) in decimal form.
3. The time \( t \) is 9 months, which is \( \frac{9}{12} = 0.75 \) years.
Now we can set up the equation:
\[
A = 1,200 + 1,200 \times 0.025 \times 0.75
\]
Therefore, the correct choice that represents this equation is:
\[
x = 1,200 + 1,200(0.025)(0.75)
\]