Question

Ralph Chase plans to sell a piece of property for $165000. He wants the money to be paid off in two ways - a short-term note at 10% interest and a

long-term note at 7% interest. Find the amount of each note if the total annual interest paid is $14250.

P

Note Ir

Amount R

165000 -

The amount of the 10% note is $ and the amount of the 7% note is $[

Answer 1

The amount of the 10% note is $90,000 and the amount of the 7% note is $75,000

Explanation:

Let the amount paid on the 7% note be $x and the amount paid on the 10% note be $y

we know that the sum of both is 165,000

Thus, mathematically

x + y = 165,000 •••••••(i)

Now let’s take a look at interest paid

For the 7%;

7/100 * x = 0.07 * x = 0.07x

For the 10%

10/100 * y = 0.1 * y = 0.1y

The addition of both gives $14,250

0.07x + 0.1y = 14,250 •••••(ii)

We now solve both equations simultaneously

From equation 1, we can have;

x = 165,000 -y

we can substitute this into ii

0.07(165,000-y) + 0.1y = 14,250

11,550 -0.07y + 0.1y = 14,250

0.03y = 14,250-11,550

0.03y = 2700

y = 2700/0.03

y = $90,000

Recall;

x = 165,000-y

x = 165,000 -90,000

x = $75,000