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?

Question

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)

Answer 1

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:

\[ x = 1,200 + 1,200(0.025)(0.75) \]