Question

You have $750,000 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 2.2% annually and Fund B pays 7.2% annually. How should you divide your money between Fund A and Fund B to produce an annual interest income of $46,500?

Answer 1

To divide $750,000 in an IRA to yield an annual interest income of $46,500, set up a system of equations to solve for the amounts to invest in Fund A (2.2% annual return) and Fund B (7.2% annual return). The equations are x + y = 750,000 and 0.022x + 0.072y = 46,500.

Step-by-step explanation:

To determine how to divide your $750,000 between Fund A and Fund B to produce an annual interest income of $46,500, we can set up a system of linear equations. If you invest x dollars in Fund A and y dollars in Fund B, the total amount invested in both funds should equal the total amount in your Individual Retirement Account (IRA).

So, our first equation is: x + y = 750,000.

The second equation is derived from the total desired annual income from the investment: 0.022x + 0.072y = 46,500.

Solving this system of equations, we get two equations with two unknowns:

Equation 1: x + y = 750,000 (Total money invested)

Equation 2: 0.022x + 0.072y = 46,500 (Desired annual interest)

By solving these simultaneously (either using substitution or elimination method), you can find the exact amounts to be invested in each fund to reach your annual income goal.