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 ​$14100

Answer 1

Explanation:

Let's denote the amount of the short-term note as "x" and the amount of the long-term note as "y."

We are given the following information:

The total amount to be paid for the property is $165,000.

The total annual interest paid is $14,100.

The short-term note has an interest rate of 10%.

The long-term note has an interest rate of 7%.

To calculate the amounts of each note, we can set up a system of equations based on the given information:

Equation 1: x + y = $165,000 (equation for the total amount)

Equation 2: 0.10x + 0.07y = $14,100 (equation for the total interest)

Now, we can solve this system of equations using substitution or elimination.

Let's solve it using elimination:

Multiply Equation 1 by -0.10 to make the coefficients of "x" cancel each other out:

-0.10x - 0.10y = -$16,500

Add this equation to Equation 2:

(-0.10x - 0.10y) + (0.10x + 0.07y) = -$16,500 + $14,100

Simplifying:

-0.03y = -$2,400

Divide both sides by -0.03 to solve for y:

y = $2,400 / 0.03

y = $80,000

Now substitute the value of y into Equation 1 to solve for x:

x + $80,000 = $165,000

x = $165,000 - $80,000

x = $85,000

Therefore, the amount of the short-term note (at 10% interest) is $85,000, and the amount of the long-term note (at 7% interest) is $80,000.