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5) Dr. Willians had $10,000 invested at s% How many dollars would he have to invest at 8% so that his total interest per year would equal 7% of the two investments?

User Twogoods
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Answer

Dr. Willians will need to invest $20,000 at 8% so that his total interest on the two investments will be 7% of the two investments.

Step-by-step explanation

If any amount, P, is invested at a rate of R%, the interest on top will be calculated as

Interest = (PR/100)

Let the amount of money invested at 8% be x dollars

The amount of interest generated on $10,000 at a rate of 5% will be

Interest = (5 × 10,000)/100 = 500 dollars

Amount of interest generated on x dollars at 8% is

Interest = (8 × x)/100 = 0.08x

Total interest on the two investments = (500 + 0.08x) dollars

We are then told that this total interest has to be 7% of the two investments (10,000 + x) dollars

This total interest can then be calculated as

Total Interest = 7% × (10,000 + x)

= 0.07 (10,000 + x)

= (700 + 0.07x) dollars

Equating these to each other

(500 + 0.08x) = (700 + 0.07x)

500 + 0.08x = 700 + 0.07x

0.08x - 0.07x = 700 - 500

0.01x = 200

Divide both sides by 0.01

(0.01x/0.01) = (200/0.01)

x = 20,000 dollars

Hope this Helps!!!

User Sreenuvasulu
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