Question 1044639
The formulas I like to use are:
(1) {{{ A[1] = P*( 1 + r[1]*t ) }}} for simple interest
(2) {{{ A[2] = P*( 1 + r[2]/n )^(nt) }}} for compound interest
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Equal amounts were invested, so instead of {{{ P }}} in
these formulas, I will use {{{ P/2 }}} in each one.
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There are 2 different interest rates:
{{{ r[1] = .06 }}} for simple interest 
{{{ rt[2] = .05 }}} for compound interest
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{{{ t = 2 }}}
{{{ n = 1 }}} 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:
{{{ (P/2)*( 1 + r[2]/n )^(nt) - P/2 }}}
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Using formula (1), the interest earned is:
{{{ (P/2)*( r[1]*t ) }}}
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Now I can say:
{{{ (P/2)*(r[1]*t) - (P/2)*( 1 + r[2]/n )^(n*t) + P/2 = 486.56 }}}
{{{ (P/2)*( .06*2) - (P/2)*( 1 + .05/1 )^(1*2) + P/2 = 486.56 }}} 
{{{ (P/2)*( 1 + .12 ) -  (P/2)*( 1 + .05 )^(1*2) = 486.56 }}}
{{{ (P/2)*1.12 - (P/2)*1.05^2 = 486.56 }}}
{{{ (P/2)*( 1.12 - 1.1025 ) = 486.56 }}}
{{{ P*.0175 = 2*486.56 }}}
{{{ P = 973.12/.0175 }}}
{{{ P = 55606.86 }}}
The total amount invested was $55,606.86
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check answer:
{{{ I[1] =  (P/2)*( r[1]*t ) }}}
{{{ I[1] = 27803.43*.06*2 }}}
{{{ I[1] = 3336.41 }}}
and
{{{ I[2] =  (P/2)*( 1 + r[2]/n )^(nt) - P/2 }}}
{{{ I[2] = 27803.43*( 1 + .05 )^2 - 27803.43 }}}
{{{ I[2] = 27803.43*1.05^2 - 27803.43 }}}
{{{ I[2] = 27803.43*1.1025 - 27803.43 }}}
{{{ I[2] = 27803.43*.1025 }}}
{{{ I[2] = 2849.85 }}}
and
{{{ 3336.41 - 2849.85 = 486.56 }}}
OK
You might want a 2nd opinion, too. There are probably 
better ways to do it, but, hopefully, I got the 
right answer.