To find out how much money was in the account after [tex]\(2 \frac{1}{2}\)[/tex] years, we'll break down the problem step-by-step using the given information about simple interest.
1. Identify the principal amount (P):
James deposited [tex]\(\$ 575\)[/tex].
2. Determine the annual simple interest rate (r):
The annual interest rate given is [tex]\(5.5 \%\)[/tex]. We convert this percentage to a decimal:
[tex]\[ r = \frac{5.5}{100} = 0.055 \][/tex]
3. Identify the time in years (t):
The time period is [tex]\(2 \frac{1}{2}\)[/tex] years, which can be written as a decimal:
[tex]\[ t = 2.5 \text{ years} \][/tex]
4. Calculate the simple interest (I):
The formula for simple interest is:
[tex]\[ I = P \times r \times t \][/tex]
Substituting in the known values:
[tex]\[ I = 575 \times 0.055 \times 2.5 \][/tex]
5. Calculate the total amount in the account after 2.5 years:
To find the total amount in the account, we add the interest to the principal amount:
[tex]\[ \text{Total Amount} = P + I \][/tex]
6. Round the total amount to the nearest cent:
The numerical result of these calculations gives us:
- The interest accrued, [tex]\(I = 79.0625\)[/tex]
- The total amount in the account, [tex]\( \text{Total Amount} = 654.0625 \)[/tex]
- Rounded to the nearest cent, the total amount is [tex]\( \$ 654.06 \)[/tex]
So, the total amount in the account after [tex]\( 2 \frac{1}{2} \)[/tex] years, rounded to the nearest cent, is:
[tex]\[ \$ 654.06 \][/tex]
Enter your answer in the box:
[tex]\[
\boxed{654.06}
\][/tex]
