Naugatuck Valley Community College MATH 123 

Kelly has M$= 24000 to invest. She wants to diversify into three investments: the first one yields p₁₌ 3% simple interest, the second one yields p₂=6% simple interest. The third one yields p₃=8% simple interest. Kelly wishes to earn $r= 1347.90 per year income. Also she wants her investment into the first option to be $N=3000 more than her investment in the third one. How much money should Kelly place in each investment?

She has to place

____ into the first choice

____ into the second choice

____ into the third choice

round to the nearest integer.

 

Answer:

$3210 into the first choice

$20580 into the second choice

$210 into the third choice

Step-by-step explanation

The amount Kelly should invest in each option is given as follows:

we introduce and define a variable x as the amount in the third option as follows:

Total = $24000

option 1 = x + 3000

option 2 = 24000-x - (x+300) = 21000 - 2x

option 3 = x

we use the interest rates and the amounts given above to solve for x as follows:

interest in one year= principal * rate

interest = 1347.90

therefore,

1347.90 = 0.03(x+3000) + 0.06(21000-2x) + 0.08 * x

1347.90 = 0.03x + 90 + 1260 - 0.12x + 0.08x

1347.90 - 1350 = 0.03x-0.12x + 0.08x

-2.1 = -0.01x

x = -2.1/-0.01

x = $210

therefore,

option 1 = x + 3000 = $3210

option 2 = 24000-x - (x+300) = 21000 - 2x = $20580

option 3 = x = $210

therefore,

$3210 into the first choice

$20580 into the second choice

$210 into the third choice