How do you solve investments problems?

Question

A rollover IRA of $18,250 was invested in two mutual funds, one earning 12% interest and the other earning 10%. After 1 year, the combined interest income is $1,956. How much was invested at each rate?

Answer 1

Hi Adam,

 

Let's begin by assigning letters to represent our two unknowns:

    x = amount invested at 12%

    y = amount invested at 10%

 

Now let's write two equations to solve for our two unknowns:

    Equation #1 (based on investment amounts):

        x + y = 18,250

    Equation #2 (based upon interest amounts):

        0.12(x) + (0.10)(y) = 1,956

 

Now let's use Equation #1 to express one unknown in terms of the other:

    x + y = 18,250

          y = 18,250 - x

 

Now let's use our "x" expression for unknown (y) and plug it into Equation #2 and solve for unknown (x):

    (0.12)(x) + (0.10)(y) = 1,956

    (0.12)(x) + (0.10)(18,250 - x) = 1,956

    0.12x + 1,825 - 0.10x = 1,956

    0.12x - 0.10x = 1,956 - 1,825

    0.02x = 131

          x = 131/0.02

          x =  $6,550 (amount invested at 12%)

 

Now let's plug our answer for unknown (x) into Equation #1 and solve for unknown (y):

    x + y = 18,250

    6,550 + y = 18,250

                y = 18,250 - 6,550

                y = $11,700 (amount invested at 10%)

 

Finally, we can verify our answers by plugging them into Equation #2 to see that both sides balance:

    (0.12)(x) + (0.10)(y) = 1,956

    (0.12)(6,550) + (0.10)(11,700) = 1,956

    786 + 1,170 = 1,956

             1,956 = 1,956 (both sides balance)

 

Since both sides balance, we are confident that our answers are correct.

 

The rule of thumb for solving word problems is to identify the unknowns, then write algebraic expressions to represent each unknown and finally set up equations to solve for each unknown.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan. 

Answer 2

To solve this, you can create a system of equations with $x in the fund with 12% interest and $y in the fund earning 10% interest. Then we can calculate total interest as follows:

.12x+.10y=1956

 

The total amount invested is 18250 so we can then say:

x+y=18250

 

We'll need to eliminate one variable to find the other so I'm going to multiply the second equation by -.10 to remove the .10y in the first equation:

-.10x-.10y=-1825

 

And add it to the first equation:

.02x=131

x=6550

 

This means they invested 6550 in the fund getting 12% and 18250-6550=11700 in the fund yielding 10%.

 

Checking our math:

6550(.12)+11700(.10)=1956.

 

Hope that helps!