Barbara invests $2400 in the National Bank at 5%. How much

Hi All,

We're told that Barbara invests $2400 in the National Bank at 5%. We're asked how much additional money she must invest at 8% so that the TOTAL annual income will be equal to 6% of her TOTAL investment. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

To start, the $2400 invested at 5% would earn ($2400)(.05) = $120.

Since Barbara invested $2400 at 5%, IF she were to invest another $2400 at 7%, then the average return for the total investment would be exactly 6% (since the EQUAL investments at 5% and 7% would 'average out' to 6%. Here though, she's investing money at 8% - which means that she would NOT need $2400 invested there (she would need LESS than that, since the investment is at a higher rate). Thus, the answers are narrowed down to either $1000 or $1200.

Let's TEST Answer A = $1200
IF... $1200 were invested at 8%, then
that investments would earn (1200)(.08) = $96
the total money invested would equal $2400 + $1200 = $3600
the total return on the investment would be $120 + $96 = $216

1% of $3600 = $36
6% of $3600 = $216
This is an exact match for what we were told, so this MUST be the answer.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote:Source: GMAT Paper Tests

Barbara invests $2400 in the National Bank at 5%. How much additional money must she invests at 8% so that the total annual income will be equal to 6% of her entire investment?

A. 1200
B. 3000
C. 1000
D. 3600
E. 2400

The OA is A.

Say Barbara invests an additional sum of $x.

Now the situation is this: She has to earn a total of 6% on investment $(2400 + x)

Since she gets an interest of 5% of the first investment ($2400), she needs to earn an additional interest of 1% (= 6% – 5%) on $2400 from $x investment. Needless to state that she has to earn 8% on $x too.

Thus,

8% of x = 6% of x + 1% of 2400

8x = 6x + 2400; cancelling %

2x = 2400

x = $1200

The correct answer: A

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: GMAT Paper Tests

Barbara invests $2400 in the National Bank at 5%. How much additional money must she invests at 8% so that the total annual income will be equal to 6% of her entire investment?

A. 1200
B. 3000
C. 1000
D. 3600
E. 2400

We can let x = the amount of money invested at 8%, making her entire investment equal to (2,400 + x). We can create the following equation:

0.05(2,400) + 0.08x = 0.06(2,400 + x)

120 + 0.08x = 144 + 0.06x

0.02x = 24

2x = 2400

x = 1,200

Answer: A