A trust account manager has $220,000 to be invested. The investment choices have current yields of 8%, 7%, and 10%. Suppose that the investment goal is to earn interest of $16,600, and risk factors make it prudent to invest some money in all three investments. If $30,000 is invested at 10%, how much will be invested at each of the other rates?
A)$50,000 at 8%; $140,000 at 7%;
B)$20,000 at 8%; $170,000 at 7%;
C)$30,000 at 8%; $160,000 at 7%;
D)$10,000 at 8%; $180,000 at 7%;
E)$40,000 at 8%; $150,000 at 7%

Question

A trust account manager has $220,000 to be invested. The investment choices have current yields of 8%, 7%, and 10%. Suppose that the investment goal is to earn interest of $16,600, and risk factors make it prudent to invest some money in all three investments. If $30,000 is invested at 10%, how much will be invested at each of the other rates? ​
A)$50,000 at 8%; $140,000 at 7%;
B)$20,000 at 8%; $170,000 at 7%;
C)$30,000 at 8%; $160,000 at 7%;
D)$10,000 at 8%; $180,000 at 7%;
E)$40,000 at 8%; $150,000 at 7%

Quizplus · Accepted Answer

Let x be the amount invested at 8%, and y be the amount invested at 7%. Then we have:

x + y + 30000 = 190000    (total amount invested is $220,000 - $30,000 = $190,000)
0.08x + 0.07y + 0.10(30000) = 16600   (total interest earned should be $16,600)

Simplifying the first equation, we get:

x + y = 160000

Subtracting 0.10(30000) = 3000 from both sides of the second equation and then multiplying everything by 100, we get:

8x + 7y = 133000

Now we can use substitution or elimination to solve for x and y. Using elimination by multiplying the first equation by 7 and subtracting from the second equation, we get:

8x + 7y = 133000
-(7x + 7y = 112000)
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x = 21000

Substituting x = 21000 into the first equation, we get:

21000 + y = 160000
y = 139000

Therefore, $21,000 should be invested at 8%, $139,000 should be invested at 7%, and $30,000 should be invested at 10%.

This corresponds to choice C.

A Trust Account Manager Has $220,000 to Be Invested