Kim T.

asked • 09/12/14# Find the amount invested at each rate

Larry Mitchell invested part of his $17000 advance at 5% annual simple interest and the rest 6% annual simple interest. If his total yearly interest from both accounts was $870, find the amount invested at each rate.

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## 3 Answers By Expert Tutors

Phillip R. answered • 09/12/14

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Average interest rate = 100 x 870/17000

Amount at 5% = (17000)(6 - 100 x 870/17000) = $15,000

Amount at 6% = $2,000

Interest = Principle*Rate*Time

When you split the principle into two parts and invest each part at a different rate:

Interest = (Part of Principle)*(One Rate)*(Time) + (Rest of the Principle)*(Other Rate)*(Time)

Let x = the amount of the Principle invested at 5%. The amount invested at 6% is $17,000 - x.

$870 = (x)*(0.05)*(1 year) + ($17,000 - x)*(0.06)*(1 year)

$870 = 0.05x + $1020 - 0.06x

-$150 = -0.01x

Solve for x.

Dattaprabhakar G. answered • 09/12/14

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Kim:

Let the "rest" of his investment be$ P

Interest on $17000 = (17000)(0.05) = 850.

Interest on $P = (0.06) P

Total interest = 850 + (0.06) P

This total is given to be $870. Solve for P, 850 + (0.06)P = 870. That is P = 20/(0.06) = $333.33 (to 2 decimals).

Answer: 17000.00 at 5%

333.33 at 6% ( to 2 decimals)

Dr. G.

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Dattaprabhakar G.

09/12/14