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

Answer:

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 = $\dfrac{\textrm Principal\times \textrm Rate\times \textrm Time}{100}$

Or, 16650 = $\dfrac{\textrm x\times \textrm 9\times \textrm 1}{100}$ + $\dfrac{\textrm (165000 - x)\times \textrm 11\times \textrm 1}{100}$

Or, 16650 = $\frac{9 x}{100}$ + $\frac{(165000- x) 11}{100}$

Or, 16650×100 = 9 x + 1815000 - 11 x

Or, 11 x - 9 x = 1815000 - 1665000

Or , 2 x = 150,000

∴ x = $\frac{150000}{2}$ = $ 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