Question

Country Day's scholarship fund receives a gift of $ 135000. The money is invested in stocks, bonds, and CDs. CDs pay 3.75 % interest, bonds pay 3.5 % interest, and stocks pay 9.7 % interest. Country day invests $ 60000 more in bonds than in CDs. If the annual income from the investments is $ 6337.5 , how much was invested in each vehicle

Answer 1

Explanation:

Let X be the amount invested in CDs, Y be the amount invested in bonds, and Z be the amount invested in stocks.

We know from the problem that:

X + Y + Z = 135000 ---(1) (the total amount invested is $135000)

0.0375X + 0.035Y + 0.097Z = 6337.5 ---(2) (the total annual income from the investments is $6337.5)

Y = X + 60000 ---(3) (the amount invested in bonds is $60000 more than the amount invested in CDs)

We can use equation (3) to substitute for Y in equations (1) and (2), then solve for X and Z as follows:

X + (X + 60000) + Z = 135000

2X + Z = 75000

0.0375X + 0.035(X + 60000) + 0.097Z = 6337.5

0.0725X + 0.097Z = 8550

Using the system of equations 2X + Z = 75000 and 0.0725X + 0.097Z = 8550, we can solve for X and Z to get:

X = 22500

Z = 78000

Substituting back into equation (3), we get:

Y = X + 60000 = 82500

Therefore, the amounts invested in CDs, bonds, and stocks were $22500, $82500, and $78000 respectively.