how much was invested in each vehicle?

Question

Country Day's scholarship fund receives a gift of $ 120000. The money is invested in stocks, bonds, and CDs. CDs pay 5.25 % interest, bonds pay 4.8 % interest, and stocks pay 6.9 % interest. Country day invests $ 30000 more in bonds than in CDs. If the annual income form the investments is $ 7087.5

Answer 1

Let the amounts invested be c (CDs), s (stocks), b (bonds), then b=c+30000 and c+s+b=120000.

After a year: 0.0525c+0.048b+0.069s=7087.5. Substituting for b we have:

0.0525c+0.048(c+30000)+0.069s=7087.5 and c+s+c+30000=120000, so 2c+s=90000, and s=90000-2c.

Substituting for s we have: 0.0525c+0.048c+1440+0.069(90000-2c)=7087.5.

0.1005c+1440+6210-0.138c=7087.5; 562.5=0.0375c, so c=$15000. Therefore b=$45000 and s=$60000.
 

The amounts invested are: $45000 in bonds; $15000 in CDs; $60000 in stocks.