Michael perez deposited a total of $3000 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 $224 in interest during a single year, how much did he deposit in each institution?

Define

x = dollars deposited into bank A.

y = dollars deposited into bank B.

Then

x + y = 3000 (1)

Assume that the compounding interval is monthly, and calculate interest earned.

Bank A:

Amount after 1 year is

A = x (1 + 0.06/12) ¹² = 1.0617x

Profit = 0.0617x

Bank B:

Amount after 1 year is

A = y (1 + 0.08/12) ¹² = 1.083y

Profit = 0.083y

The total profit for 1 year is $224, therefore

0.0617x + 0.083y = 224 (2)

From (1), obtain

y = 3000 - x (3)

Substitute (3) into (2).

0.0617x + 0.083 (3000 - x) = 224

-0.0213x = - 25

x = 1173.70

y = 3000 - x = 1826.30

Answer:

Michael deposited $1,173.70 into bank A and $1,826.30 into bank B.