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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) $2,240
b) $3,120
c) $4,480
d) $5,760

User Ladessa
by
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1 Answer

6 votes

Final answer:

After calculating based on the information given, it was found that George needs to invest an additional $13,080 at 4% simple interest to achieve an overall 5% return on both investments combined. This figure does not match any of the multiple-choice answers provided, indicating there may be an error in the calculation or provided options.

Step-by-step explanation:

When George invested $8,720 in an account that pays 7.5% simple interest and he wants to find out how much additional money must be invested at 4% simple interest for the average return on the two investments to be 5%, we can set up an equation to solve for the unknown amount, let's call it x.

Let the total investment be $8,720 + x. The total interest from both investments should equal the amount you would get if the total investment was earning 5%. So,

0.075 * $8,720 + 0.04 * x = 0.05 * ($8,720 + x)

We can simplify and solve for x:

$654 + 0.04x = 0.05 * $8,720 + 0.05x

$654 + 0.04x = $436 + 0.05x

Now, subtract 0.04x from both sides:

$654 = $436 + 0.01x

Subtract $436 from both sides:

$218 = 0.01x

Divide both sides by 0.01 to find x:

x = $21,800

To find the additional amount that needs to be invested at 4%, we subtract the original amount George invested from x:

x = $21,800 - $8,720 = $13,080

This amount is not one of the answers provided. It is possible that there is a mistake in the calculation or in the information given, but based on the calculation above, $13,080 would be the additional amount that needs to be invested at 4% simple interest to achieve an average return of 5% on the total investment.

User Bheru Lal Lohar
by
8.5k points

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