Question

An executive invests $23,000, some at 7% and the rest at 6% annual interest. If he receives an annual return of $1,480, how much is invested at each rate?

Answer 1

The investments were made as follows:

$10,000 at 7% interest
$13,000 at 6% interest

Explanation:

First remember that percentages are to be divided by 100 before any calculations can be made

So 7% = 0.07

8% = 0.08

Let x be the amount invested at 7% and y be the amount invested at 8%

We have:

x + y = 23000 (total amount is $23000)

Return on x = 0.07x

Return on y = 0.06y

Total return is

0.07x + 0.06y = 1480

The two equations are

x + y = 23000 [1]
0.07x + 0.06y = 1480 [2]

To solve for x and y,

multiply [1] x 0.07

=> 0.07x + 0.07y = 0.07(23000)

=> 0.07x + 0.07y = 1610 [3]

Since the coefficients of x are the same we can subtract [2] from [3] to eliminate the x term and solve for y

[3] - [2]:

(0.07x + 0.07y ) - (0.07x + 0.06y) = 1610 - 1480

0.07x + 0.07y - 0.07x - 0.06y = 130

Collecting like terms

0.07x-0.07x +0.07y - 0.06y = 130

0.01y = 130

y = 130/0.01 = 13000

x = 23000 - 13000 = 10000

Therefore the investments were made as follows:

$10,000 at 7% interest
$13,000 at 6% interest