Country Day's scholarship fund receives a gift of $ 145000.

Question

Country Day's scholarship fund receives a gift of $ 145000. The money is invested in stocks, bonds, and CDs. CDs pay 2.75 % interest, bonds pay 3 % interest, and stocks pay 6.8 % interest. Country day invests $ 35000 more in bonds than in CDs. If the annual income from the investments is $ 6567.5 , how much was invested in each vehicle?

Answer 1

Let S = amount invested in stocks

Let B = amount invested bonds

Let C = amount invested in CDs

S + B + C = 145000

.068S + .03B + .0275C = 6567.5

B = C + 35000

S + C + 35000 + C = 145000

S + 2C + 35000 = 145000

S + 2C = 110000

S = 110000 - 2C

.068(110000 - 2C) + .03(C + 35000) + .0275C = 6567.5

7480 - .136C + .03C + 1050 + .0275C = 6567.5

8530 - .0785C = 6567.5

-.0785C = -1962.5

C = 25000

B = 25000 + 35000

B = 60000

S = 110000 - 2(25000)

S = 11000 - 50000

S = 60000

Now checking everything

60000 + 60000 + 25000 = 110000

110000 = 110000

.068(60000) + .03(60000) + .0275(25000) = 6567.5

4080 + 1800 + 687.5 = 6567.5

6567.5 = 6567.5

$60000 is invested in stocks

$60000 is invested in bonds

$25000 is invested in CDs