Question

a total of $52,000 is invested in two municipal bonds that pay 4.75% and 6.25% simple interest. the investor wants an annual interest income of $2890 from the investments. what amount should be invested in the 4.75% bond?

Answer 1

To find the amount that should be invested in the 4.75% bond, set up a system of equations based on the total investment and desired annual interest income. Simplify and solve the equation to find the value of x, which represents the amount invested in the 4.75% bond. The answer is $24,000.

Step-by-step explanation:

To find the amount that should be invested in the 4.75% bond, we can set up a system of equations based on the total investment and the desired annual interest income.

Let x represent the amount invested in the 4.75% bond.

The amount invested in the 6.25% bond would be the total investment of $52,000 minus x.

From the given information, we can set up the following equation:

x(4.75%) + (52,000 - x)(6.25%) = $2,890

Simplify and solve the equation to find the value of x:

0.0475x + 0.0625(52,000 - x) = 2,890

0.0475x + 3,250 - 0.0625x = 2,890

0.0475x - 0.0625x = 2,890 - 3,250

-0.015x = -360

x = 24,000

Therefore, $24,000 should be invested in the 4.75% bond.