Question

Jim invested $4000 in two accounts. The first account paid 10% interest. the second account paid 2% interest. At end of the year, he had earned $192 in interest. How much was in each account?

Answer 1

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