Betsy Rhone

Answered question

2021-12-21

You had $10,000 to invest. You put x dollars in a safe, government-insured certificate of deposit paying 5% per year. You invested the remainder of the money in noninsured corporate bonds paying 12% per year. Your total interest earned at the end of the year is given by the algebraic expression $0.05x+0.12\left(10,000-x\right)$. a. Simplify the algebraic expression. b. Use each form of the algebraic expression to determine your total interest earned at the end of the year if you invested$6000 in the safe, government-insured certificate of deposit.

Answer & Explanation

hysgubwyri3

Beginner2021-12-22Added 43 answers

Step 1
Given that we have to invest 10,000 and put x dollars in a self government -insured certificate that pays 5% and then invests rest of the money in corporate bonds that pays 12% interest. So the total interest earned at the end of the year is given by the function $0.05x+0.12\left(10000-x\right)$.
We need to:
1) simplify the algebraic expression.
2) find the interest earned at the end of year if 6000 is invested in safe government insured certificate.
Step 2
1) First let us simplify the expression.
Let $y=0.05x+0.12\left(10,000-x\right)$
$y=0.05x+1200-0.12x$
$y=1200-0.07x$ is the simplified expression.
Step 3
2) if 6000 invested in the safe government insured certificate of deposit.
So $x=6000$.
$y=1200-0.07\left(6000\right)$
$y=1200-420$
$y=780$.
So the interest earned at the end of the year is 780.

Hattie Schaeffer

Beginner2021-12-23Added 37 answers

Step 1
To determine the total interest earned at the end of the year if we invested 6000$in the safe, government-insured certificate of deposit, we should use the simplification that we did in the answer of part (a) and we replace x by$6000
Step 2
$1200-0.07x=1200-\left(0.07\cdot 6000\right)$
$=1200-420$
$=\mathrm{}780$

nick1337

Expert2021-12-28Added 777 answers

To simplify out the expression, we can distribute the multiplication over addition. (one of the properties)
$0.05x+1200-0.12x$
$=1200-0.07x$
We can use the equation we just determined to plug in 6000 for x to find the total interest.
$1200-0.07\cdot \left(6000\right)=780$

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