To determine the best balance after investing $12,000 for 7 years, we will calculate the final amounts for both simple interest and compound interest.
Simple Interest Calculation
The formula for simple interest is:
\[ A = P + (P \times r \times t) \]
Where:
- \(A\) = Total amount after interest
- \(P\) = Principal amount ($12,000)
- \(r\) = Interest rate (5% or 0.05)
- \(t\) = Time in years (7)
Calculating:
\[ A = 12000 + (12000 \times 0.05 \times 7) \] \[ A = 12000 + (12000 \times 0.35) \] \[ A = 12000 + 4200 \] \[ A = 16200 \]
Compound Interest Calculation
The formula for compound interest is:
\[ A = P(1 + r)^t \]
Where:
- \(A\) = Total amount after interest
- \(P\) = Principal amount ($12,000)
- \(r\) = Interest rate (4.5% or 0.045)
- \(t\) = Time in years (7)
Calculating:
\[ A = 12000(1 + 0.045)^7 \] \[ A = 12000(1.045)^7 \] Calculating \(1.045^7\):
\[ 1.045^7 \approx 1.34885 \]
Now substituting back:
\[ A = 12000 \times 1.34885 \approx 16186.20 \]
Conclusion
- Final amount with simple interest at 5%: $16,200.00
- Final amount with compound interest at 4.5%: $16,186.20
Thus, the best balance after 7 years will be:
\[ \boxed{16200.00} \]