Let's calculate the interest earned from both options to determine which one is better for Aria.
Simple Interest Calculation
The formula for simple interest is: \[ I = P \times r \times t \] where:
- \( I \) is the interest,
- \( P \) is the principal amount (initial investment),
- \( r \) is the rate of interest per year (as a decimal),
- \( t \) is the time in years.
For the simple interest at 6.5%:
- \( P = 6700 \)
- \( r = 0.065 \)
- \( t = 3 \)
Calculating the interest: \[ I = 6700 \times 0.065 \times 3 = 6700 \times 0.195 = 1309.50 \]
Compound Interest Calculation
The formula for compound interest is: \[ A = P(1 + r)^t \] where \( A \) is the amount of money accumulated after n years, including interest. The interest earned is \( A - P \).
For the compound interest at 6%:
- \( P = 6700 \)
- \( r = 0.06 \)
- \( t = 3 \)
Calculating the amount: \[ A = 6700(1 + 0.06)^3 = 6700(1.191016) \approx 7977.83 \] Now, calculating the interest earned: \[ I = A - P = 7977.83 - 6700 \approx 1277.83 \]
Comparison of Simple and Compound Interest
- Simple Interest Earnings (6.5%): \( 1309.50 \)
- Compound Interest Earnings (6%): \( 1277.83 \)
Finding the Difference
\[ \text{Difference} = 1309.50 - 1277.83 = 31.67 \]
Conclusion
Aria should invest with the 6.5% simple interest because it will result in $31.67 more in interest earnings than the 6% compound interest over 3 years.
None of the provided answer options are accurate based on these calculations.