To determine how much William had in the account after 6 years, we need to use the compound interest formula:
[tex]\[ A(t) = P(1 + i)^t \][/tex]
where:
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( i \)[/tex] is the annual interest rate,
- [tex]\( t \)[/tex] is the number of years the money is invested.
Given:
- Principal [tex]\( P = \$6000 \)[/tex]
- Annual interest rate [tex]\( i = 5.5\% = 0.055 \)[/tex]
- Number of years [tex]\( t = 6 \)[/tex]
Let's plug in these values into the compound interest formula and solve step-by-step.
1. Identify the principal amount, interest rate, and number of years:
- Principal [tex]\( P = 6000 \)[/tex]
- Interest rate [tex]\( i = 0.055 \)[/tex]
- Number of years [tex]\( t = 6 \)[/tex]
2. Substitute the values into the formula:
[tex]\[ A(6) = 6000(1 + 0.055)^6 \][/tex]
3. Calculate inside the parentheses first:
[tex]\[ 1 + 0.055 = 1.055 \][/tex]
4. Raise 1.055 to the power of 6:
[tex]\[ 1.055^6 \approx 1.379 \][/tex]
5. Multiply the result by the principal amount:
[tex]\[ 6000 \times 1.379 \approx 8273.06 \][/tex]
After following these steps, the amount in William's account after 6 years is approximately \[tex]$8273.06.
Therefore, the correct answer is:
B. \$[/tex]8273.06
