Question

reggie means invested part of $31,000 in municipal bonds that earn 6.5% annual simple interest and the remainder of the money in 7.5% corporate bonds. how much is invested in each account if the total annual interest earned is $2,155? at 6.5% $ at 7.5% $

Explanation:

Step1: Let the amount invested at 6.5% be $x$.

The amount invested at 7.5% is $(31000 - x)$.

Step2: Calculate the interest from each investment.

The interest from the 6.5% - investment is $0.065x$. The interest from the 7.5% - investment is $0.075(31000 - x)$.

Step3: Set up the equation based on the total interest.

$0.065x+0.075(31000 - x)=2155$.

Step4: Expand and simplify the equation.

$0.065x + 2325-0.075x=2155$.
Combining like - terms gives: $2325-(0.075x - 0.065x)=2155$, or $2325 - 0.01x=2155$.

Step5: Solve for $x$.

Subtract 2325 from both sides: $-0.01x=2155 - 2325=-170$.
Then divide both sides by $- 0.01$: $x=\frac{-170}{-0.01}=17000$.

Step6: Find the amount invested at 7.5%.

The amount invested at 7.5% is $31000 - 17000 = 14000$.

Answer:

at 6.5%: $17000
at 7.5%: $14000