SOLUTION: Suppose $50,000 is divided into two bank accounts. One account pays 4% simple interest per year and the other pays 6.4%. After five years there is a total of $12,000 in interest be

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Suppose $50,000 is divided into two bank accounts. One account pays 4% simple interest per year and the other pays 6.4%. After five years there is a total of $12,000 in interest be      Log On

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Question 1133695: Suppose $50,000 is divided into two bank accounts. One account pays 4% simple interest per year and the other pays 6.4%. After five years there is a total of $12,000 in interest between the two accounts. How much was invested into the bank account that pays 4% simple interest (rounded to the nearest cent)?
Found 2 solutions by addingup, josmiceli:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
0.04x + 0.064(50,000-x) = 12,000/5
0.04x + 3,200 - 0.064x = 2,400
-0.024x = -800
x = 33,333.33 this is the money invested at 4%
50,000-33,333.33 = 16,666.67
~~~~~~~~~~~~~~~~~~~~~
Check:
The formula for simple interest is Prt
33,333.33 * 0.04 * 5 = 6,666.67
16,666.67 * 0.064 *5 = 5,333.33
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Total . . . . . . . . 12,000 Correct

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
For simple interest:
+I%5B1%5D+=+P%5B1%5D%2Ar%5B1%5D%2At+
+I%5B2%5D+=+P%5B2%5D%2Ar%5B2%5D%2At+
+I%5B1%5D+%2B+I%5B2%5D+=+12000+
+P%5B1%5D+%2B+P%5B2%5D+=+50000+
+r%5B1%5D+=+.04+
+r%5B2%5D+=+.064+
+t+=+5+
-----------------------------
+I%5B1%5D+=+P%5B1%5D%2A.04%2A5+
(1) +I%5B1%5D+=+.2P%5B1%5D+
and
+12000+-+I%5B1%5D+=+%28+50000+-+P%5B1%5D+%29%2A.064%2A5+
+12000+-+I%5B1%5D+=+%28+50000+-+P%5B1%5D+%29%2A.32+
+12000+-+I%5B1%5D+=+16000+-+.32P%5B1%5D+
(2) +I%5B1%5D+=+.32P%5B1%5D+-+4000+
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Substitute (1) into (2)
+.2P%5B1%5D+=+.32P%5B1%5D+-+4000+
+.12P%5B1%5D+=+4000+
+P%5B1%5D+=+33333.33+
+P%5B2%5D+=+50000+-+33333.33+
+P%5B2%5D+=+16666.67+
-----------------------------------
$33,333.33 is invested in 4% interest account
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check:
(1) +I%5B1%5D+=+.2%2A33333.33+
(1) +I%5B1%5D+=+6666.67+
and
(2) +I%5B1%5D+=+.32P%5B1%5D+-+4000+
(2) +6666.67+=+.32%2A33333.33+-+4000+
(2) +6666.67+=+10666.67+-+4000+
(2) +6666.67+=+6666.67+
OK