Question

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.

Answer 1

To help Aria decide on the best investing option for her college fund, we calculated the future values of her $6,700 investment using both simple interest at 6.5% and compound interest at 6% over 3 years. The simple interest option yields a future value of $8,006.65, while the compound interest option results in $7,979.81. The simple interest investment outperforms the compound interest by $26.84 over the 3-year period.

Step-by-step explanation:

The student's question is about comparing the future values of an investment of $6,700 made with simple interest at a rate of 6.5% annually and compound interest at a rate of 6% annually over a period of 3 years. To provide a clear answer, we will calculate the future value for both scenarios and then find the difference.

For simple interest, the formula is Future Value = Principal × (1 + (Interest Rate × Time)). Plugging in the values gives us:

Future Value = $6,700 × (1 + (0.065 × 3))

Future Value = $6,700 × (1 + 0.195)

Future Value = $6,700 × 1.195

Future Value = $8,006.65

For compound interest, the formula is Future Value = Principal × (1 + Interest Rate)Time. Using the compound interest formula:

Future Value = $6,700 × (1 + 0.06)^3

Future Value = $6,700 × (1.06)^3

Future Value = $6,700 × 1.191016

Future Value = $7,979.81

The difference in the future values stemming from the two types of interest is thus:

Difference = $8,006.65 (simple interest) - $7,979.81 (compound interest)

Difference = $26.84

Therefore, in this case, investing in an account with simple interest results in a higher future value compared to the compound interest option over a 3-year period, by $26.84.

Answer 2

Aria would earn more with simple interest than compound interest over 3 years: $1,305.5 versus $824.01, respectively. The difference in her earnings with simple interest compared to compound interest would be $481.49.

Step-by-step explanation:

Aria is trying to decide between investing her savings of $6,700 in a simple interest account at 6.5% or a compound interest account at 6% for 3 years. To assist Aria, we need to calculate the difference in interest earned between the two options.

For simple interest, the calculation is straightforward:

I = P * r * t

Where I is the interest, P is the principal amount, r is the interest rate, and t is the time (in years).

Using Aria's values:

I = $6,700 * 0.065 * 3

I = $1,305.5

This means Aria would earn $1,305.5 in simple interest over 3 years.

For compound interest, the formula is a bit more complex:

A = P(1 + r/n)^(nt)

Where A is the amount after interest, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year (annually in this case, so n=1), and t is the time in years.

Using Aria's values:

A = $6,700(1 + 0.06/1)^(1*3)

A = $6,700(1.06)^3

A = $7,524.01

The interest earned with compound interest is A - P, which is $7,524.01 - $6,700 = $824.01.

The difference between the compound interest and simple interest is therefore $824.01 - $1,305.5 = -$481.49. This means that with simple interest, Aria would earn $481.49 more over 3 years.