Question

George invested $8,720 in an account that pays 7.5% simple interest. How much additional money must be invested in an account that pays 4% simple interest so that the average return on the two investments amounts to 5%?

a) $4,360
b) $5,120
c) $6,240
d) $7,180

Answer 1

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.