Solve the problem.
-Jancie has $180,000 to invest to obtain annual income. She wants some of it invested in safe Certificates of Deposit yielding 5%. The rest she wants to invest in AA bonds yielding 12% per year. How much should she
Invest in each to realize exactly $18,100 per year?
A) $120,000 at 5% and $60,000 at 12%
B) $130,000 at 5% and $50,000 at 12%
C) $140,000 at 12% and $40,000 at 5%
D) $130,000 at 12% and $50,000 at 5%

Question

Quizplus · Accepted Answer

Let's call the amount invested in CDs "x" and the amount invested in AA bonds "y". We can set up two equations based on the given information:

0.05x + 0.12y = 18,100
x + y = 180,000

We can solve for one variable in terms of the other in the second equation, and substitute that into the first equation:

x = 180,000 - y
0.05(180,000 - y) + 0.12y = 18,100
9,000 - 0.05y + 0.12y = 18,100
0.07y = 9,100
y = 130,000

So Jancie should invest $130,000 in AA bonds and the remaining $50,000 in CDs. This will give her an annual income of:

0.05($50,000) + 0.12($130,000) = $6,500 + $15,600 = $18,100

Therefore, the best choice is D. Let x be the amount invested in AA bonds yielding 12%. Then the amount invested in CDs yielding 5% is 180,000 - x. The annual income from the AA bonds is 0.12x and the annual income from the CDs is 0.05(180,000 - x). We want the sum of these two incomes to be equal to $18,100 per year:
0.12x + 0.05(180,000 - x) = 18,100
0.12x + 9,000 - 0.05x = 18,100
0.07x = 9,100
x = 130,000
Therefore, Jancie should invest $130,000 in AA bonds yielding 12% and $50,000 in CDs yielding 5%. This will result in an annual income of:
0.12(130,000) + 0.05(50,000) = 15,600 + 2,500 = $18,100. 
This is the only choice that meets the given criteria.

Solve the Problem. -Jancie Has $180,000 to Invest to Obtain Annual Income. She