Michael Perez deposited a total of $2000 with two savings institutions. Bank A pays interest at the rate of 6%/year, whereas Bank B pays interest at the rate of 8%/year. If Michael earned a total of $136 in interest during a single year, how much did he deposit in each institution?

He invested $1200 in bank A and $800 in bank B.

Step-by-step explanation:

Let x represent the amount deposited in bank A.

Let y represent the amount deposited in bank B

Michael Perez deposited a total of $2000 with two savings institutions. This means that

x + y = 2000

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

Considering the amount invested in bank A,

P = x

R = 6%

T = 1 year

I = (x × 6 × 1)/100 = 0.06x

Considering the amount invested in bank B,

P = y

R = 8%

T = 1 year

I = (y × 8 × 1)/100 = 0.08y

If Michael earned a total of $136 in interest during a single year, it means that

0.06x + 0.08y = 136 - - - - - - - - - - -1

Substituting x = 2000 - y into equation 1, it becomes

0.06(2000 - y) + 0.08y = 136

120 - 0.06y + 0.08y = 136

- 0.06y + 0.08y = 136 - 120

0.02y = 16

y = 16/0.02 = 800

x = 2000 - y = 2000 - 800

x = 1200

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