Question

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​?

Answer 1

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

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