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

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

addition

step-by-step explanation: