To determine how much you will have in the account at the beginning of the 7th year with a simple interest rate of [tex]\(2\%\)[/tex] per year, we can follow these steps:
1. Identify the variables in the given formula:
- Principal ([tex]\(P\)[/tex]): \[tex]$4500 (initial deposit)
- Annual interest rate (\(r\)): 0.02 (2%)
- Number of years (\(n\)): 7
2. Insert these values into the equation:
\[
A(n) = 4500 + (n-1)(0.02 \cdot 4500)
\]
3. Substitute \(n\) with 7:
\[
A(7) = 4500 + (7-1)(0.02 \cdot 4500)
\]
4. Simplify inside the parentheses:
\[
A(7) = 4500 + 6(0.02 \cdot 4500)
\]
5. Calculate the interest amount for one year:
\[
0.02 \cdot 4500 = 90
\]
6. Multiply this interest amount by the number of years minus one (since interest compounds on the initial amount):
\[
6 \cdot 90 = 540
\]
7. Add the interest obtained over 6 years to the principal amount:
\[
A(7) = 4500 + 540 = 5040
\]
8. Round the result to the nearest dollar if necessary (in this case, it remains the same):
\[
A(7) = 5040
\]
Therefore, at the beginning of the 7th year, you will have \$[/tex]5040 in the account.
So, the correct answer is A. \$5040.
