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 11% and a long term note at 9% interest find the amount of each note if the total annual interest paid is 16650

Answer 1

To find the amount of each note, set up a system of equations using the given information. Solve the system to determine the values of x and y, which represent the amounts of each note.

Step-by-step explanation:

To find the amount of each note, we need to set up a system of equations. Let's represent the amount of the short term note as 'x' and the amount of the long term note as 'y'.

The interest paid for the short term note would be 0.11x, and the interest paid for the long term note would be 0.09y. The total annual interest paid is given as $16,650, so we can set up the equation:

0.11x + 0.09y = 16,650

We also know that the total amount of the property is $165,000, so we can set up another equation:

x + y = 165,000

Solving these two equations will give us the values of x and y, which represent the amounts of each note.

Answer 2

The Principal amount for 9 % is $ 75,000 And

The Principal amount for 11 % is $ 90,000 .

Step-by-step explanation:

Given as :

The principal amount = $165000

Total interest paid = SI = $16650

The two rate of interest are 9% and 11%

The Time period of loan = 1 year

Let The Principal for 9% = $ x

And The Principal for 11% = $ 165000 - $x

From Simple Interest method

Simple Interest =
`(\textrm Principal* \textrm Rate* \textrm Time)/(100)`

Or, 16650 =
`(\textrm x* \textrm 9* \textrm 1)/(100)` +
`(\textrm (165000 - x)* \textrm 11* \textrm 1)/(100)`

Or, 16650 =
`(9 x)/(100)` +
`((165000- x) 11)/(100)`

Or, 16650×100 = 9 x + 1815000 - 11 x

Or, 11 x - 9 x = 1815000 - 1665000

Or , 2 x = 150,000

∴ x =
`(150000)/(2)` = $ 75,000

And $ 165000 - $ 75000 = $ 90,000

Hence The Principal amount for 9 % is $ 75,000 And

The Principal amount for 11 % is $ 90,000 . Answer