Question

you have $250,000 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 4.0% annually and fund b pays 6.5% annually. how should you divide your money between fund a and fund b to produce an annual interest income of $11,250? you should invest $\square$ in fund a and $\square$ in fund b.

Explanation:

Step1: Define variables

Let $x$ be the amount invested in Fund A (in dollars), then the amount invested in Fund B is $(250000 - x)$ dollars.

Step2: Set up the interest equation

The interest from Fund A is $0.04x$ (since it pays 4.0% annually), and the interest from Fund B is $0.065(250000 - x)$ (since it pays 6.5% annually). The total interest is $11250$, so we have the equation:
$$0.04x + 0.065(250000 - x) = 11250$$

Step3: Solve the equation

First, expand the second term:
$$0.04x + 16250 - 0.065x = 11250$$
Combine like terms:
$$-0.025x + 16250 = 11250$$
Subtract $16250$ from both sides:
$$-0.025x = 11250 - 16250$$
$$-0.025x = -5000$$
Divide both sides by $-0.025$:
$$x = \frac{-5000}{-0.025} = 200000$$

Step4: Find the amount for Fund B

The amount invested in Fund B is $250000 - x = 250000 - 200000 = 50000$

Answer:

You should invest $\$200000$ in Fund A and $\$50000$ in Fund B.