Answer:
Hence The amount invested for 5 years is $ 7000 , and The amount invested for 7 years is $ 12000
Step-by-step explanation:
Given as :
The amount invested in treasury note for 5 years = $ x
the time period = 5 year
The rate of interest applied = 2.8 % at simple interest
So, From simple Interest method :
Simple Interest = [tex]\dfrac{\textrm Principal \times \textrm Rate\times \textrm Time}{100}[/tex]
or, [tex]SI_1[/tex] = [tex]\dfrac{\textrm x \times \textrm 2.8\times \textrm 5}{100}[/tex]
Or, [tex]SI_1[/tex] = 0.14 x
Again ,
The amount invested in treasury note for 10 years = $ x + $ 5000
the time period = 10 year
The rate of interest applied = 3.6 % at simple interest
So, From simple Interest method :
Simple Interest = [tex]\dfrac{\textrm Principal \times \textrm Rate\times \textrm Time}{100}[/tex]
or, [tex]SI_2[/tex] = [tex]\dfrac{\textrm( x + 5000) \times \textrm 3.6\times \textrm 10}{100}[/tex]
Or. [tex]SI_2[/tex] = 0.36 x + 1800
Now , ∵ The total amount of interest from both investment = $ 5300
So, [tex]SI_1[/tex] + [tex]SI_2[/tex] = $ 5300
or, 0.14 x + 0.36 x + $ 1800 = $ 5300
Or, 0.5 x = $ 5300 - $ 1800
or, 0.5 x = 3500
∴ x = [tex]\frac{3500}{0.5}[/tex]
I.e x = $ 7000
Hence The amount invested for 5 years is $ 7000 , and The amount invested for 7 years is $5000 + $ 7000 = $ 12000 Answer
