Question

A $86 ,000 trust is to be invested in bonds paying 9% , CDs paying 6% , and mortgages paying 10% . The bond and CD investment together must equal the mortgage investment. To earn a $7180 annual income from the investments, how much should the bank invest in bonds?

Answer 1

to earn a $7180 annual income from the investments, the bank needs to invest $10,000 into the bonds.

Explanation:

Let the mortgage investment be X

The Bond to be Y

and the CDs to be Z

Thus;

X+Y+Z = 86000 ------- (1)

Y + Z = X ------------(2)

10X + 9Y + 6Z = 7180 × 100 ------ (3)

So;we now have:

X+Y+Z = 86000 ------- (1)

Y + Z = X ------------(2)

10X + 9Y + 6Z = 718000 ------ (3)

Let ; replace X with Y+Z in equation (1) and (3)

Y+Z + Y+Z = 86000

2Y + 2Z = 86000

Divide both sides by 2

Y+Z = 43000 ------ (4)

From equation (3)

10X + 9Y + 6Z = 718000

10(Y+Z) + 9Y + 6Z = 718000

10Y +10Z + 9Y +6Z = 718000

19Y + 16Z = 718000 -----(5)

Y+Z = 43000 ------ (4)

19Y + 16Z = 718000 -----(5)

Using elimination method; multiply (-16) with equation (4) and (5) ; so, we have:

-16 Y -16 Z = -688000

19Y + 16Z = 718000

3Y + 0 = 30000

3Y = 30000

Y = 30000/3

Y = 10000

From (4);

Y+Z = 43000

So; replace Y with 10000; we have:

10000 + Z = 43000

Z = 43000 - 10000

Z = 33000

From (1) ;

X+Y+Z = 86000

X + 10000 + 33000 = 86000

X + 43000 = 86000

X = 86000 - 43000

X = 43000

Since we assume the bond to be Y and Y = $10000;

Thus; to earn a $7180 annual income from the investments, the bank needs to invest $10,000 into the bonds.