Answer: the amounts are $1400 and $2600
Step-by-step explanation:
Let x represent the amount in the first account.
Let y represent the amount in the second account.
Jim invested $4000 in two accounts. It means that
x + y = 4000
The interest on the amount invested is simple interest. The formula for simple interest is expressed as
I = PRT/100
Where
I is the interest
P is the principal or initial amount
R is the interest rate
T is the time
Considering the first account,
P = x
R = 10%
T = 1
I = (x × 10 × 1 )/100 = 10/100 = 0.1x
Considering the second account
P= y
R = 2%
T = 1
I = (y × 2 × 1)/100 = 0.02y
At end of the year, he had earned $192 in interest. It means that
0.1x + 0.02y = 192 - - - - - - -1
Substituting x = 4000 - y into equation 1, it becomes
0.1(4000 - y) + 0.02y = 192
400 - 0.1y + 0.02y = 192
- 0.1y + 0.02y = 192 - 400
-0.08y = -208
y = -208/0.08 = $2600
x = 4000 - y
x = 4000 - 2600 = $1400
