Question 1044639: Sara invested equal amounts-one at 6% simple interest and the other at 5% compound interest. If the former earns $486.56 as more interest at the end of two years, find the total amount invested
Found 3 solutions by Alan3354, josmiceli, MathTherapy:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Sara invested equal amounts-one at 6% simple interest and the other at 5% compound interest. If the former earns $486.56 as more interest at the end of two years, find the total amount invested
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A = amount invested.
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A*0.06 - A*0.05 = 486.56/2
0.01A = 243.28
A = $24328
Answer by josmiceli(19441)  (Show Source):
You can put this solution on YOUR website! The formulas I like to use are:
(1)  for simple interest
(2)  for compound interest
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Equal amounts were invested, so instead of  in
these formulas, I will use  in each one.
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There are 2 different interest rates:
 for simple interest
 for compound interest
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 because the period for compounding
must be 1 year. ( nothing else was specified )
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I'm a little confused by " $486.56 as more interest "
Is the $486.56 the actual interest earned at 6% simple interest?
Or, is that amount the difference in interest earned between
simple and compound?
I'll take a guess by removing the word "as", so $486.56
will be the difference
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Using formula (2), the interest earned is:
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Using formula (1), the interest earned is:
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Now I can say:
The total amount invested was $55,606.86
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check answer:
and
and
OK
You might want a 2nd opinion, too. There are probably
better ways to do it, but, hopefully, I got the
right answer.
Answer by MathTherapy(10557)  (Show Source):
You can put this solution on YOUR website! Sara invested equal amounts-one at 6% simple interest and the other at 5% compound interest. If the former earns $486.56 as more interest at the end of two years, find the total amount invested
Let amount invested in each be P
Simple interest, @ 6%, for 2 years: P * 2 * .06, or .12P
Simple interest, @ 5%, for 2 years: P * 2 * .05, or .1P
Since the 6% earned $486.56 more than the 5%, then we get: .12P - .1P = 486.56
.02P = 486.56
P, or principal invested in EACH = 
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