Country Day invested in stocks. Country Day invested in bonds. Country Day invested in CDs.

Question

Country Day's scholarship fund receives a gift of $ 165000. The money is invested in stocks, bonds, and CDs. CDs pay 5 % interest, bonds pay 5.6 % interest, and stocks pay 9 % interest. Country day invests $ 20000 more in bonds than in CDs. If the annual income from the investments is $ 10470 , how much was invested in each vehicle?

Answer 1

Let the money invested be denoted by following

x_S - money invested in stocks

x_B - money invested in bonds

x_C - money invested in CDs

We know that the total amount invested (received as a gift) is $165000

With the above, we can come up with an overall equation

x_S+x_B+x_C = 165000 (Eqn 1)

We also know that Country day invests $ 20000 more in bonds than in CDs, so

x_B= x_C+20000 (Eqn 2)

Eqn 1 will now become

x_S+x_C+20000+x_C = 165000

or x_S+2x_C+20000= 165000 (Eqn 3)

From this we also get, the money invested in stocks in terms of the money invested in CDs

x_S= 165000-(2x_C+20000) = 145000-2x_C (Eqn 4)

The last equation we need to solve this is the annual income from the interest which is $10470

I_S - Interest income from stocks investment = 9% X x_S = 0.09x_S

I_B - Interest income from bonds investment = 5.6% X x_B = 0.056x_B

I_C - Interest income from CDs investment = 5.0% X x_c = 0.05x_C

I_S + I_B + I_C = 10470

0.09x_S + 0.056x_B + 0.05x_C = 10470 (Eqn 5)

When we plug in value of x_B from Eqn 2 and x_S from Eqn 4 in Eqn 5 above we get

0.09 (145000-2x_C) + 0.056 (x_C+20000) + 0.05 (x_C) = 10470

We solve for x_C to get

x_C = $50000

x_B= x_C+20000 = $70000

x_S= 145000-2x_C = $45000