Ed Moura has ​$52000 invested in stocks paying 7​%. How much additional money should he invest in certificates of deposit paying 4​% so that the average return on the two investments is ​5%?
He should invest ​? enter your response here in certificates of deposit.
​(Simplify your answer. Type an integer or a​ decimal.)

Respuesta :

The computation shows that the additional money that should be invested is $104000.

How to calculate the value?

Based on the information given, the equation to solve the question will be:

Amount invested = $52000

The additional investment needed will be represented by b. Therefore,

7%(52000) + (4% × b) = 5%(b + 52000)

0.07(52000) + 0.04b = 0.05(b + 52000)

3640 + 0.04b = 0.05b + 2600

Collect like terms

0.05b - 0.04b = 3640 - 2600

0.01b = 1040

Divide to get the value of b

b = 1040/0.01

b = 104000

Therefore, the additional money that should be invested is $104000.

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He should invest ​ $104,000 in certificates of deposit.

What is Ed Moura's average return?

Ed Moura's average return is the sum of the two returns multiplied by the proportion of total invested in each investment, in other words, the average return is the weighted average return

let amount invested in certificates of deposit be X

total investment=$52,000+X

average return=(7%*$52,000/$52,000+X)+(4%+X/$52,000+X)

average return=5%

5%=(7%*$52,000/$52,000+X)+(4%+X/$52,000+X)

5%=($3,640/$52,000+X)+(0.04X/$52,000+X)

$52,000+X is common

5%=($3640+0.04X)/$52,000+X

5%*($52,000+X)=$3640+0.04X

$2600+0.05X=$3640+0.04X

0.05X-0.04X=$3640-$2600

0.01X=$1040

X=$1040/0.01

X=$104,000

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