Question

You have 750,000 IRA at time you retire. You have the option of investing this money in two funds. Funds A pays 1.3% annually and Fund B pays 6.3% annually. How should you divide your money between A and B to produce an annual interest income of $37,750

Answer 1

Sounds like a system of equations, that is my opinion at a glance, I have not delved any further.

Answer 2

thats what i thought but cant find the steps to complete it in my textbook

Answer 3

Is this simple or compound interest?

Answer 4

to be honest im not even sure
i got for fund A- 560000 and fund B- 190000

Answer 5

Then let's assume simple. I haven't solved for anything on my own yet, but here's the setup so far. Let's say you take x amount of dollars from the total $750,000 and put it into Fund A. So, you're left with (750,000-x) to put into Fund B.

The balances of Funds A and B will be given by A_1 and A_2, respectively.
\[A_1=P_1(1+r_1t)\\A_2=P_2(1+r_2t),\]
where A is the balance after time t,
P = initial balance/deposit,
r = (annual simple) interest rate, and
t = time (which we'll leave as 1 year).

So, you have
\[A_1=x(1+0.013)\\
A_2=(750,000-x)(1+0.063)\]
Does the setup make sense?

Answer 6

yes

Answer 7

So, after one year, the balance of the accounts is
\[\begin{align*}A_1+A_2&=1.013x+1.063(750,000-x)\\
&=797,250-0.05x\end{align*}\]

Answer 8

Since you're working with simple interest, you'll be using the formula
\[I=Prt\]
In this case, P = A_1 + A_2 and t = 1.

One minor change, though. A_1 and A_2 have different rates associated with each other, so you'll have to write the interest equation as
\[I=(A_1r_1+A_2r_2)\]
Do you follow?