To determine the amount James will have in his account after 6 years, we need to use the compound interest formula. The compound interest formula is:
[tex]\[ A(t) = P \cdot (1 + r)^t \][/tex]
where:
- [tex]\( A(t) \)[/tex] is the amount of money accumulated after [tex]\( t \)[/tex] years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money).
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal).
- [tex]\( t \)[/tex] is the time the money is invested for in years.
Given the information:
- The principal amount [tex]\( P \)[/tex] is \[tex]$20,000.
- The annual interest rate \( r \) is 8.3%, which can be written as a decimal \[0.083\].
- The duration \( t \) is 6 years.
Substituting these values into the formula, we get:
\[ A(6) = 20,000 \cdot (1 + 0.083)^6 \]
This matches option B from the given choices. Therefore:
\[ \text{Correct equation: } A(6) = 20,000 \cdot (1 + 0.083)^6 \]
Using this equation and solving it, James will have approximately \$[/tex]32,270.13 in his account after 6 years.
