Respuesta :
Answer:
The Loan amount at 11 % interest rate is $ 18,500 And
The Loan amount at 9 % interest rate is $ 19,000
Step-by-step explanation:
Given as :
Let The loan given at interest rate of 11 % annual = $ x
And The loan given at interest rate of 9 % annual = ($37,500 - $ x)
Total interest fro both loan = $3745
I.e CI 1 + CI 2 = $3745
Now, From compound interest method :
[tex]Amount= Principal\times (1 + \frac{Rate}{100})^{Time}[/tex]
[tex]A 1 = $ 1\times (1 + \frac{11}{100})^{1}[/tex]
Or, A 1 = $ 1.11 x
Similarly
[tex]A 2 = ($37,500 -x ) \times (1 + \frac{9}{100})^{1}[/tex]
Or, A 2 = 1.09 × ($37,500 - $ x)
∵ Compound Interest = Amount - principal
Or, $ 3745 = CI 1 + CI 2
Or, $ 3745 = ($ 1.11 x - $ x) + ( 1.09 × ($37,500 - $ x) - ($37,500 - $ x) )
Or, $ 3745 = $ .11 x+ ($37,500 - $ x) ( .09 )
Or, $ 3745 = $ .02 x + $ 3375
or, 0.02 x = $ 3745 - $ 3375
∴ x = $ [tex]\frac{370}{.02}[/tex]
SO, x = $ 18,500
And $ 37500 - x = $ 19,000
Hence The Loan amount at 11 % interest rate is $ 18,500 And
The Loan amount at 9 % interest rate is $ 19,000 Answer
