SOLUTION: An executive invests $21,000, some at 8% and the rest at 6% Annual interest. if he receive an annual return of &1,620, how much is invested at each rate At 8% interest = At 6% i

Algebra.Com
Question 1163731: An executive invests $21,000, some at 8% and the rest at 6% Annual interest. if he receive an annual return of &1,620, how much is invested at each rate
At 8% interest =
At 6% interest =
Found 3 solutions by MathLover1, MathTherapy, greenestamps:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!


let be amount at % and at %
...solve for
.........eq.1
% = interest of and %= interest of gives us an annual return of & :
....eq.2
----------------------------------substitute from eq.1 in eq.2

....eq.2..solve for





go to
.........eq.1...substitute


so,
at % interest =&
at % interest =&


check:
....eq.2



->true



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

An executive invests $21,000, some at 8% and the rest at 6% Annual interest. if he receive an annual return of &1,620, how much is invested at each rate
At 8% interest =
At 6% interest =
Let amount invested at 8% be E

Then amount invested at 6% = 21,000 - E

We then get: .08E + .06(21,000 - E) = 1,620

.08E + 1,260 - .06E = 1,620

.08E - .06E = 1,620 - 1,260

.02E = 360

Amount invested in the 8%-fund, or 

You should now be able to find the amount invested in the 6% fund. 

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!
 


If a formal algebraic solution is not required, here is a quick and easy solution method.


(1) All $21,000 at 6% would yield $1260 interest; all at 8% would yield $1680 interest.

(2) The actual interest, $1620, is 6/7 of the way from $1260 to $1680.  (Picture the three numbers on a number line -- 1260, 1620, and 1680.  1260 to 1680 is 420; 1260 to 1620 is 360; 360/420 = 6/7.)

(3) That means 6/7 of the total was invested at the higher rate.


ANSWER: 6/7 of the $21,000, or $18,000, was invested at 8%; the other $3000 was invested at 6%.


CHECK: .06(3000)+.08(18000) = 180+1440 = 1620


 

RELATED QUESTIONS


An executive invests $28,000, some at 6% and the rest at 4% annual interest. If he... (answered by ikleyn,greenestamps)

An executive invests $28,000, some at 8% and some at 6% annual interest. If he receives... (answered by stanbon)

An executive invests $21,000, some at 8% and some at 6% annual interest. If he receives... (answered by addingup,MathTherapy)

An executive invests $25,000, some at 8% and the rest at 6% annual interest. If he... (answered by ikleyn)

An executive invests $10,000,some at 9% and some at 8% annual interest. If he receives an  (answered by stanbon)

An executive invests $26,000, some at 8% and some at 4% annual interest. If he receives... (answered by mananth)

An executive invests $28,000, some at 8% and some at 4% annual interest. If he receives... (answered by TimothyLamb)

An executive invests 22000, some at 7% and some at 6% annual interest. If he receives an... (answered by Fombitz)

An executive invests $22,000, some at 6% and some at 4% annual interest. If he receives... (answered by mananth)