Aria is investing $6,700 of her savings from her summer job for her college fund. She is planning to invest the amount for 3 years and can choose between simple interest at 6.5% and compound interest at 6%. Find the difference between the two interest earning types to help Aria decide which investing option is best for her.(1 point) Responses Aria should invest with 6% compound interest because it will result in $73.81 more in interest earnings. Aria should invest with 6% compound interest because it will result in $73.81 more in interest earnings. Aria should invest with 6.5% simple interest because it will result in $26.69 more in interest earnings. Aria should invest with 6.5% simple interest because it will result in $26.69 more in interest earnings. Aria should invest with 6.5% simple interest because it will result in $187.26 more in interest earnings. Aria should invest with 6.5% simple interest because it will result in $187.26 more in interest earnings. Aria should invest with 6% compound interest because it will result in $86.76 more in interest earnings. Aria should invest with 6% compound interest because it will result in $86.76 more in interest earnings.

1 answer

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.