Investment. A trust account manager has $240,000 to be invested. The investment

Question

Investment. A trust account manager has $240,000 to be invested. The investment choices have current yields of 8%, 7% and 10%. Suppose that the investment goal is to earn interest of $18,000, and risk factors make it prudent to invest some money in all three investments.

Find a general description for the amounts invested at three rates.

If $10,000 is invested at 10%, how much will be invested at each of the other rates?

What is the maximum amount that will be invested at 7%, and in this case how much will be invested at the other rates?

What is the minimum amount that will be invested at 7%, and in this case how much will be invested at the other rates?

Explanation / Answer

Total amount = $240,000

Options A = 8% , B = 7% and C =10%

Interest Goal = $18,000

a) $10,000 in 10% and X amount in A and $230,000- X in B

Total interest should be $18,000

18,000 = 10,000*10*1 /100 + X *8/100 + (230,000-X)*7/100

18000 = 1000+8X/100 + 16100 -7X/100

18000 - 17100 =X/100

X = 90000

i.e $90000 in 8% and $10,000 in 10% and $140,000 in 7%

b) for maximum in 7% in that case remaininig amount should be in 10% to complete to goal interest

x in 7 % max possible then 0 in 8% and 240,000 -X in 10%

$18,000 = 7x/1000 + ($240,000 - X)*10 /100

18000 = -3x/100 + 24000

6000 =3x/100

x = $200,000 in 7 % is maximum possible

and $40,000 in 10%

c ) min of 7 % when 0 amount in 10% and remaining in 8%

18000 = 7x/100 + (240000-x)*8/100

18000 = -x/100 + 19200

X =$120,000 in 7% and $120,000 in 8%

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