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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?

Respuesta :

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.

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