Answer:The principal for the first account is $5000
The principal for second account is $4600
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P = principal
T = time in years
R = interest rate on the principal.
Let x represent the amount invested in the first account
Let y represent the amount invested in the second account
Gabriel invests $9600 in two different accounts. This means that
x + y = 9600 - - - - - - - -1
For first account, The interest rate is 13%. The duration is one year.
Therefore
P = x
T = 1 year
R = 13%
Therefore
I = (x × 13 × 1)/100
I = 0.13x
For second account, he interest rate is 6%. The duration is one year.
Let y represent the principal for the second account. Therefore
P = y
T = 1 year
R = 6
Therefore
I = (y × 6 × 1)/100
I = 0.06y
At the end of the first year he had earned $926 in interest. This means that
0.13x + 0.06y = 926 - - - - - - - -2
Substituting x = 9600 - y into equation 2, it becomes
0.13(9600 - y) + 0.06y = 926
1248 - 0.13y + 0.06y = 926
- 0.13y + 0.06y = 926 - 1248
- 0.07y = -322
y = - 322/- 0.07 = 4600
x = 9600 - y
x = 9600 - 4600
x = 5000
