Answer:
Amount invested in account with 5% annual interest = $300
Amount invested in account with 7% annual interest = $400
Amount invested in account with 8% annual interest = $900
Step-by-step explanation:
Let the money invested in account with 5% annual interest = [tex]x[/tex]
As per question statement,
Money invested in account with 8% annual interest = [tex]3x[/tex]
Given that total amount invested in three accounts = $1600
So, Money invested in account with 7% annual interest = 1600- [tex]3x[/tex] -[tex]x[/tex] = 1600- [tex]4x[/tex]
For one year, the compound interest is same as that of Simple Interest.
Formula for simple interest is given as:
[tex]SI =\dfrac{PRT}{100}[/tex]
Where, P is the amount invested
R is the annual rate of interest
T is the time for which the amount is invested.
As per question statement:
[tex]\dfrac{x\times 5\times 1}{100}+\dfrac{(1600-4x)\times 7\times 1}{100}+\dfrac{3x\times 8\times 1}{100} =115\\\Rightarrow 5x\times +1600\times 7-28x+24x=11500\\\Rightarrow 29x-28x = 11500-11200\\\Rightarrow \bold{x =\$300}[/tex]
Amount invested in account with 5% annual interest = $300
Amount invested in account with 7% annual interest = $1600-$1200 = $400
Amount invested in account with 8% annual interest = $900
