Final answer:
The additional money that needs to be invested at a 4% simple interest rate to achieve an average return of 5% when $8,720 is invested at 7.5% is not one of the provided options. The correct amount surpasses the highest option given, amounting to $13,080, which can be calculated through an equation based on the average return desired.
Step-by-step explanation:
The student wants to know how much additional money must be invested at a 4% simple interest rate in order to achieve an average 5% return on the total investment when $8,720 is already invested at a 7.5% simple interest rate. Let the additional money required be represented by 'x'. The total interest from both investments should equate to a 5% return on the total investment.
First, we calculate the interest from the initial investment: $8,720 * 7.5% = $654.
Next, the average interest we're aiming for on the total amount would be 5% of ($8,720 + x). This gives us a total interest equation: $654 + 0.04x = 0.05($8,720 + x).
Solving this equation:
- $654 + 0.04x = 0.05 * $8,720 + 0.05x
- $654 + 0.04x = $436 + 0.05x
- $654 - $436 = 0.05x - 0.04x
- $218 = 0.01x
- x = $218 / 0.01
- x = $21,800
However, we're interested in how much additional money must be invested, not total, so we subtract the already invested $8,720 from this total:
- x = $21,800 - $8,720
- x = $13,080
Therefore, none of the options (a, b, c, d) are correct.