Question

Country Day's scholarship fund receives a gift of $ 195000. The money is invested in stocks, bonds, and CDs. CDs pay 2.25 % interest, bonds pay 5.2 % interest, and stocks pay 7.8 % interest. Country day invests $ 35000 more in bonds than in CDs. If the annual income from the investments is $ 11040 , how much was invested in each vehicle?

Answer 1

$11,300 is invested in CDs

$46,300 is invested in bonds

$107,400 is invested in stocks

*I rounded to the nearest hundred

Step-by-step explanation:

S = money invested in stocks

B = money invested in bonds

C = money invested in CDs

S + B + C = 165,000

B = C + 35,000

0.078S + 0.052B + 0.0225C = 11,040

S + C + 35,000 + C = 165,000

S + 2C = 130,000

0.078S + 0.052(C + 35,000) + 0.0225C = 11,040

0.078S + 0.052C + 1,820 + 0.0225C = 11,040

0.078S + 0.0745C = 9,220

S + 2C = 130,000

(0.078S + 0.0745C = 9,220) x 1 / 0.078

S + 2C = 130,000

S + 0.96C = 118,205

2C - 0.96C = 130,000 - 118,205

1.04C = 11,795

C = 11,341 ≈ 11,300 (approximate number due to rounding errors)

B = 11,300 + 35,000 = 46,300

S = 165,000 - 46,300 - 11,300 = 107,400