Question

Question

Find the best balance after investing $12,000 for a period of 7 years at two different interest earning types: simple interest at 5% and compound interest at 4.5%. Round the answer to two decimal places.(1 point)
The best balance after investing $12,000 for a period of 7 years is $
.

Answer 1

To find the best balance after investing $12,000 for 7 years with simple and compound interest, we will calculate both:

1. Simple Interest

The formula for simple interest is: \[ A = P(1 + rt) \] where:

• \( A \) is the final amount,
• \( P \) is the principal amount (initial investment),
• \( r \) is the annual interest rate (in decimal),
• \( t \) is the time in years.

For this investment:

• \( P = 12000 \)
• \( r = 0.05 \) (5%)
• \( t = 7 \)

Substituting the values: \[ A = 12000(1 + 0.05 \times 7) = 12000(1 + 0.35) = 12000 \times 1.35 = 16200 \]

2. Compound Interest

The formula for compound interest is: \[ A = P(1 + r)^t \] where:

• \( A \) is the final amount,
• \( P \) is the principal amount,
• \( r \) is the annual interest rate (in decimal),
• \( t \) is the number of years.

For this investment:

• \( P = 12000 \)
• \( r = 0.045 \) (4.5%)
• \( t = 7 \)

Substituting the values: \[ A = 12000(1 + 0.045)^7 = 12000(1.045)^7 \]

Calculating \( (1.045)^7 \): \[ (1.045)^7 \approx 1.348850 (using a calculator) \]

Now substitute back: \[ A \approx 12000 \times 1.348850 \approx 16186.20 \]

Conclusion

Now we compare both interests:

• Simple interest balance: $16,200
• Compound interest balance: $16,186.20

The best balance after investing $12,000 for a period of 7 years is:

\[ \boxed{16200.00} \]