SOLUTION: A mother wants to invest $9,000.00 for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% and the remainder

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Question 1067717: A mother wants to invest $9,000.00 for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% and the remainder ina. Savings bond that earns 7%. If the total interest earned after one year is $540.00 , how much money was invested in the CD account ?
Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x@4%
9000-x@7%
.04x+(.07)(9000-x)=540
-0.03x=630=540
-0.03x=-90
3x=9000
x=$3000@4%=$120 ANSWER is $3000 in CD at 4%
9000-x=$6000@7%=$420
They sum to $540.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use the formula +I+=+P%2Ar%2At+
where +t+=+1+ yr
---------------------
For interest on the CD:
+I%5B1%5D+=+P%5B1%5D%2Ar%5B1%5D%2At+
+I%5B1%5D+=+P%5B1%5D%2A.04%2A1+
(1) +I%5B1%5D+=+.04P%5B1%5D+
------------------------------
For interest on the savings bond:
+I%5B2%5D+=+P%5B2%5D%2Ar%5B2%5D%2At+
+I%5B2%5D+=+%28+9000+-+P%5B1%5D+%29%2A.07%2A1+
+I%5B2%5D+=+.07%2A9000+-+.07%2AP%5B1%5D+
(2) +I%5B2%5D+=+630+-+.07P%5B1%5D+
-------------------------------
(3) +I%5B1%5D+%2B+I%5B2%5D+=+540+
(3) +I%5B2%5D+=+540+-+I%5B1%5D+
-------------------------------
Plug (1) into (3)
(3) +I%5B2%5D+=+540+-+.04P%5B1%5D+
Plug (3) into (2)
(2) +540+-+.04P%5B1%5D+=+630+-+.07P%5B1%5D+
(2) +.03P%5B1%5D+=+90+
(2) +P%5B1%5D+=+3000+
and
(1) +I%5B1%5D+=+.04P%5B1%5D+
(1) +I%5B1%5D+=+.04%2A3000+
(1) +I%5B1%5D+=+120+
------------------------
$3,000 was invested in the CD account
------------------------------------
check:
+P%5B1%5D+%2B+P%5B2%5D+=+9000+
+P%5B2%5D+=+9000+-+3000+
+P%5B2%5D+=+6000+
and
+I%5B2%5D+=+540+-+I%5B1%5D+
+I%5B2%5D+=+540+-+120+
+I%5B2%5D+=+420+
and
+I%5B2%5D+=+P%5B2%5D%2Ar%5B2%5D%2At+
+420+=+6000%2A.07+
+420+=+420+
OK