Question

Ralph Chase plans to sell a piece of property for ​$160000. He wants the money to be paid off in two ways a ​short-term note at ​11% interest and a​ long-term note at ​8% interest. Find the amount of each note if the total annual interest paid is ​$15350.

Answer 1

Let x be the amount of the short-term note and y be the amount of the long-term note.

We know that the total amount of the two notes is $160,000:

x + y = 160,000

We also know that the total annual interest paid is $15,350:

0.11x + 0.08y = 15,350

To solve for x and y, we can use the first equation to solve for one variable in terms of the other:

y = 160,000 - x

Substitute this expression for y in the second equation:

0.11x + 0.08(160,000 - x) = 15,350

Simplify and solve for x:

0.11x + 12,800 - 0.08x = 15,350

0.03x = 2,550

x = 85,000

Substitute this value for x in the equation y = 160,000 - x to find y:

y = 160,000 - 85,000 = 75,000

Therefore, the amount of the short-term note is $85,000 and the amount of the long-term note is $75,000.