Question

Country Day's scholarship fund receives a gift of $ 125000. The money is invested in stocks, bonds, and CDs. CDs pay 4.75 % interest, bonds pay 3.7 % interest, and stocks pay 10.9 % interest. Country day invests $ 60000 more in bonds than in CDs. If the annual income from the investments is $ 7970 , how much was invested in each vehicle?

Answer 1

Explanation:

Let's begin by assigning variables to represent the amounts invested in each vehicle.

Let x be the amount invested in CDs,

y be the amount invested in bonds, and

z be the amount invested in stocks.

From the problem statement, we know that:

x + y + z = 125000 (the total amount invested)

y = x + 60000 (the amount invested in bonds is $60000 more than in CDs)

0.0475x + 0.037y + 0.109z = 7970 (the total annual income from the investments)

We can use the second equation to substitute for y in the other two equations, giving us a system of two equations in two variables:

x + (x + 60000) + z = 125000

0.0475x + 0.037(x + 60000) + 0.109z = 7970

Simplifying the first equation, we get:

2x + 60000 + z = 125000

2x + z = 65000

Substituting z = 65000 - 2x into the second equation, we get:

0.0475x + 0.037(x + 60000) + 0.109(65000 - 2x) = 7970

Simplifying and solving for x, we get:

0.0475x + 0.037x + 0.109(65000) - 0.218x + 0.109(2x) = 7970 - 0.109(60000)

0.026x = 1730

x = 66538.46

So, $66538.46 was invested in CDs. Using the equations y = x + 60000 and z = 65000 - 2x, we can calculate that $126,538.46 was invested in bonds and $45,923.08 was invested in stocks.

Therefore, $66538.46 was invested in CDs, $126,538.46 was invested in bonds, and $45,923.08 was invested in stocks.