Annual income vs investments and interest

Question

Country Day's scholarship fund receives a gift of $ 80000. The money is invested in stocks, bonds, and CDs. CDs pay 5 % interest, bonds pay 5.8 % interest, and stocks pay 10.5 % interest. Country day invests $ 30000 more in bonds than in CDs. If the annual income from the investments is $ 5970 , how much was invested in each vehicle? 

Country Day invested $     in stocks.

Country Day invested $     in bonds. 

Country Day invested $     in CDs. 

Answer 1

Let...

S = Amount invested in stocks

B = Amount invested in bonds

C = Amount invested in CDs

80000 = S + B + C

B = 30,000 + C

80000 = S + 30,000 + C + C

80000 = S + 30000 + 2C

50000 - 2C = S

5970 = (0.105)*S + (0.058)*B + (0.05)*C

5970 = (0.105)*(50000-2C) + (0.058)*(30000+C) + (0.05)*C

5970 = 5250 - 0.21C + 1740 + 0.058C + 0.05C

5970 = 6990 - 0.102C

C = 10000

B = 30000 + C = 30000 + 10000 = 40000

B = 40000

S = 50000 - 2C = 50000 - 2*10000 = 50000 - 20000 = 30000

S = 30000

Answer:

Country Day invested $30,000     in stocks.

Country Day invested $40,000     in bonds. 

Country Day invested $10,000     in CDs.