Question

Edmonds Community College's (EDCC) scholarship fund received a gift of $ 275,000. The money is invested in stocks, bonds, and CDs. CDs pay 5.75% interest, bonds pay 3.3% interest, and stocks pay 6.1% simple interest. To better secure, the total investment EDCC invests 4 times more in CDs than the sum of the stocks and bonds investments If the annual income from the investments is $14,885, how much was invested in each vehicle? solve by the method of your choice either using reduced row echelon form of the matrix equation

Answer 1

Answer : Solving by Matrix Equation

From the given problem

there are 3 investment vehicles.i.e CDs,Bonds & Stocks

CDs pays interest of 5.75% PA

Bonds Pays interest of 3.3% PA

Stocks Pays interest of 6.1% PA

given 2 statements

1.Investment in CDs = 4 times of sum of investment in Bonds & Stocks

2.Annual income from investment =$14,885

Total inventment =$275,000

We can assume "C" is inventment in CDs, "B" is investment in Bonds & "S" is Investment in Stocks.

from the above statements,we can frame equations as follows

C+B+S=$275,000

5.75C+3.30B+6.10S=$14,855*100=$14,88,500

C=4(B+S)=4B+4S

Equations are:

Equation 1 : C+B+S=$275,000

Equation 2 : 5.75C+3.30B+6.10S=$14,88,500

Equation 3 : C=4B+4S

br placing equation 3 in equation 1 & equation 2 then the result is as follows

4B+4S+B+S=$275,000

Equation 4 : B+S=$55,000

5.75(4B+4S)+3.30B+6.10S=$14,88,500

Equation 5 : 26.30B+29.10S=$14,88,500

Solving Equation 4 & Equation 5,We can get

S=$15,000

B=$40,000

Placing above values in Equation 1

C+$15,000+$40,000=$275,000

C=$220,000

So from above

Investment in CDs is $220,000

Investment in Bonds is $40,000

Investment in Stocks is $15,000