Investment Word Problem

Question

Becky earned $48,000 from royalties on her cookbook. She paid a 28% income tax on these royalties. The balance was invested in two ways, some of it at 3.25% interest and some at 1.75%. The investments produced $904.80 interest per year. Find the amount invested at each rate.

Answer 1

Lauren,

 

First, find Becky's net income (after taxes):

 

The tax she'll pay is;

 

$48000 * 28% or $48000 * .28 = $13440.

 

Now, her net income then is:

 

$48000 - 13440 = $34560

 

This is the amount she has to invest.

 

Now, let 'x' represent the amount she invested at 3.25% and 'y' represent the amount she invested at 1.75%.

 

We can now describe the total financial situation with two equations:

 

(1) x + y = $34560 (her two investments have to equal her net income)

 

(2) 3.25% * x + 1.75% * y = $904.80 (the interest from her two investments equals $904.80)

 

We now have two equations and two unknowns; we can use substitution to solve.

 

Let eq 1 be rewritten as:

 

x = -y + 34560

 

Then substitute this value of x for x in eq 2:

 

.0325(-y + 34560) + .0175y = 904.80

 

Simplify:

 

-.0325y + 1123.20 + .0175y = 904.80

 

Combine like terms:

 

-.015y + 1123.20 = 904.80

 

Subtract 1123.20 from both sides:

 

-.015y = -218.40

 

Divide both sides by -.015:

 

y = -218.40/-.015 = $14560 (the amount she invested at 1.75%)

 

To find x, substitute this value of y for the y in eq 1:

 

x + $14560 = $34560

 

x = $34560 - $14560 = $20000 (the amount she invested at 3.25%)

 

Hope this helps!