To find out how much Jeff has in the account after 3 years with an initial investment of $3000, an interest rate of 6.5% (0.065), and compounded annually, we can use the formula for compound interest:
\[ A(t) = P(1 + I)^t \]
Where:
- \( A(t) \) is the amount after time \( t \),
- \( P \) is the principal amount (initial investment),
- \( I \) is the interest rate (in decimal form),
- \( t \) is the time in years.
Substituting in the values:
- \( P = 3000 \)
- \( I = 0.065 \)
- \( t = 3 \)
Now we can calculate:
\[ A(3) = 3000(1 + 0.065)^3 \]
\[ A(3) = 3000(1.065)^3 \]
Calculating \( (1.065)^3 \):
\[ (1.065)^3 \approx 1.207135 \]
Now substitute this back into the equation:
\[ A(3) = 3000 \times 1.207135 \approx 3621.41 \]
So, rounding to two decimal places, Jeff has approximately $3621.41 in the account after 3 years.
Among the options given, the closest answer is:
C. $3623.85