You have $250 comma 000 in an IRA (Individual Retirement Account) at the time you retire. You have the option of investing this money in two funds: Fund A pays 2.4% annually and Fund B pays 7.4% annually. How should you divide your money between Fund A and Fund B to produce an annual interest income of $9 comma 000?

$190,000 goes to fund A while $60,000 goes to fund B to earn an annual interest income of $9,000

Step-by-step explanation:

Here, we are interested in knowing the way the money should be divided between the interest rates to give an annual interest totaling $9,000.

Let’s have the amount going to Fund A as $x while $y is the amount going to Fund B.

Although, we do not know the value of these amounts, we know that they both total $250,000

Thus, mathematically;

x + y = 250,000 •••••••••••(i)

Now also, let’s work with the percentages to get the interests:

For fund A;

2.4% of x = interest

2.4/100 * x = 2.4x/100

For fund B;

7.4% * y = interest

7.4/100 * y = interest

7.4y/100 = interest

Adding both gives a total of $9,000

Mathematically, that would be;

2.4x/100 + 7.4y/100 = 9,000

Multiply through by 100;

2.4x + 7.4y = 900,000 •••••••(ii)

From i, x = 250,000 -y

Substitute this into ii

2.4(250,000-y) + 7.4y = 900,000

600,000 -2.4y + 7.4y = 900,000

Collecting like terms, we have;

7.4y-2.4y = 900,000-600,000

5y = 300,000

y = 300,000/5

y = $60,000

But x = 250,000 - y

x = 250,000 - 60,000

x = $190,000

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b