SOLUTION: Two certificates of deposits (CDs) pay interest at rates that differ by 4%. Money invested for 1 year in the first CD earns $50 interest. The same amount invested in the second CD

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Question 926636: Two certificates of deposits (CDs) pay interest at rates that differ by 4%. Money invested for 1 year in the first CD earns $50 interest. The same amount invested in the second CD earns $90. Find the two rates of interest. Thank you so much for whoever takes the time to help me.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
They don't say that it's compound interest, so
it must be a simple interest problem
Let +r+ = the rate for the 1st CD
--------------------------------
The 2nd CD earns $40 more, so it must be
a higher rate, so it is:
+r+%2B+.04+
---------------------------------
Let +A+ = amount invested at each rate
-------------------
Equation for1st rate:
(1) +A%2Ar=+50++
Equation for 2nd rate:
(2) +A%2A%28+r+%2B+.04+%29+=+90+
-------------------------
(1) +A+=+50%2Fr+
and
(2) +A+=+90%2F%28+r+%2B+.04+%29+
-------------------------
I can say:
+50%2Fr+=+90%2F%28+r+%2B+.04+%29+
+50%2A%28+r+%2B+.04+%29+=+90r+
+50r+%2B+2+=+90r+
+40r+=+2+
+r+=+1%2F20+
+r+=+.05+
and
+r+%2B+.04+=+.09+
The rates are 5% and 9%
-----------------------
check:
(1) +A+=+50%2Fr+
(1) +A+=+50%2F.05+
(1) +A+=+1000+
and
(2) +A+=+90%2F%28+r+%2B+.04+%29+
(2) +A+=+90%2F%28+.05+%2B+.04+%29+
(2) +A+=+90%2F.09+
(2) +A+=+1000+
OK