A trust account manager has $260,000 to be invested. The investment choices have

Question

A trust account manager has $260,000 to be invested. The investment choices have current yields of 8%,7%, and 10%. Suppose that the investment goal is to earn interest of $19,400 a Find a general description or the amounts invested at the three rates et x the amount invested at 8% y the amount i vested at 7% and Z the amount invested a 09 Express your answer in terms o z (b) If $17,000 is invested at 10%, how much will be invested at each of the other rates? 8% 796 What if $36,000 is invested at 10%? 89% 796 (c) what is the minimum amount that will be invested at 7%? In this case how much will be invested at the other rates? 8% 10% (d) What is the maximum amount that will be invested at 7%? In this case how much will be invested at the other rates? 896 10% Need Help?

Explanation / Answer

By given conditions we have,

x+y+z = 260000...........(i)

x*8%+y*7%+z*10% = 19400

i.e., 8x+7y+10z = 1940000........(ii)

a) Multiplying (i) by 8 and then subtracting from (ii) we get,

-y+2z = -140000

i.e., y = 2z+140000

Putting this in (i) we get,

x+2z+140000+z = 260000

i.e., x = 120000-3z

Therefore, (x,y,z) = (120000-3z,140000+2z,z).

b) Given, z = $17,000.

Then, x = $(120000-3*17000)

i.e., x = $69000

And, y = $(140000+2*17000)

i.e., y = $174000

Therefore, $69,000 and $174,000 will be invested at 8% and 7% respectively.

Given z = $36,000.

Then, x = $(120000-3*36000) = $12000

And, y = $(140000+2*36000) = $212000

Therefore, $12,000 and $212,000 will be invested at 8% and 7% respectively.

c) The minimum amount that will be invested at 7% is $140,000.

Here, y is minimum when z is minimum.

Then, z = $0.

And, x = $120000

Therefore, $120,000 and $0 will be invested at 8% and 10% respectively.

d) Here, y is maximum when x is minimum.

Then, x = $0

i.e., 120000-3z = 0

i.e., 3z = 120000

i.e., z = 120000/3

i.e., z = 40000

Then, y = $(140000+2*40000) = $220000

Therefore, the maximum amount that will be invested at 7% is $220,000.

And, $0 and $40,000 will be invested at 8% and 10% respectively.

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