SOLUTION: If an amount of $9,000 is invested at a simple interest rate of 3 1/2% interest per year, how much additional money (in dollars) must be invested at a simple interest rate of

Algebra.Com
Question 1203605: If an amount of $9,000 is invested at a simple interest rate of
3 1/2%
interest per year, how much additional money (in dollars) must be invested at a simple interest rate of 5% per year to ensure that the interest each year is 4% of the total amount invested?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52754)   (Show Source): You can put this solution on YOUR website!
If an amount of $9,000 is invested at a simple interest rate of 3 1/2% interest per year,
how much additional money (in dollars) must be invested at a simple interest rate of 5% per year
to ensure that the interest each year is 4% of the total amount invested?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let x be the value under the problem question (= an additional amount to invest at 5%).


From one side, these two amounts of $9000 and x dollars generate the total annual interest
of 0.035*19000 + 0.05x  dollars.


From the other side, we want to have the total annual interest of 0.04(9000+x)  dollars.


So, we write this equation

    0.035*9000 + 0.05x = 0.04(9000+x)   dollars.


Now simplify and find x

    0.035*9000 + 0.05x = 0.04*9000 + 0.04x

    0.05x - 0.04x = 0.04*9000 - 0.035*9000

        0.01x     =       45

            x     =       45/0.01 = 4500.


ANSWER.  An additional amount to invest at 5% is 4500 dollars.

Solved.



Answer by greenestamps(13195)   (Show Source): You can put this solution on YOUR website!


First a quick and easy informal solution method....

You are mixing 3.5% interest investments with 5% interest investments to get an overall 4% interest.

4% is twice as close to 3.5% as it is to 5%, so the amount invested at 3.5% must be twice the amount invested at 5%.

Since $9000 was invested at 3.5%, the amount invested at 5% has to be half of that, which is $4500.

ANSWER: $4500

And a standard formal algebraic solution....

3.5% of $9000, plus 5% of x, equals 4% of ($9000+x):
RELATED QUESTIONS

Ethan invested $19,000 for 1 year, part at 11% simple interest and part at 13% simple... (answered by ikleyn,mananth,Edwin McCravy,greenestamps)
If Ben invests $4000 at 4% interest per year, how much additional money must he invest at (answered by stanbon)
If ben invests $4000 at 4% interest per year, how much additional money must he invest at (answered by checkley71)
If Ben ivests $4000 at 4% interest per year,how much additional money must he invest at 5 (answered by ankor@dixie-net.com)
Susan invests R45 000 at a simple interest rate of 6% per year. Two years later, she adds (answered by )
If Ben invest $40,000 at 4% interest per year, how much additional money must he invest... (answered by lwsshak3)
If bonnie invests $24,000 at 3% interest per year, how much additional money must she... (answered by Mathtut)
An investmest of $5600 is made at an annual simple interest of 6.5%. How much additional... (answered by stanbon)
If Ben invests $4000 at 3% interest per year, how much additional money must he invest at (answered by mananth)