Question 1046232
(1)
Formula for compound interest:
{{{ A = P*( 1 + r/n )^(n*t) }}}
{{{ P = 8000 }}}
{{{ r = .06 }}}
{{{ n = 2 }}}
{{{ t = 7 }}}
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{{{ A = 8000*( 1 + .06/2 )^( 2*7 ) }}}
{{{ A = 8000*( 1.03 )^14 }}}
{{{ A = 8000*1.51259 }}}
{{{ A = 12100.72 }}}
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Formula for simple interest:
{{{ A = P*( 1 + r*t ) }}}
{{{ A = 8000*( 1 + .075*7 ) }}}
{{{ A = 8000*( 1 + .525 ) }}}
{{{ A = 12200 }}}
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The investment at 7.5% simple interest 
gives her more return
{{{ 12200 - 12100.72 = 99.28 }}} more in 7 yrs
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(2)
{{{ A = P*( 1 + r/n )^(n*t) }}}
{{{ A = 20000 }}}
{{{ r = .0625 }}}
{{{ n = 12 }}}
{{{ t = 5 }}}
{{{ 20000 = P*( 1 + .0625/12 )^(12*5) }}}
{{{ 20000 = P*( 1 + .005208 )^60 }}}
{{{ 20000 = P*1.36573 }}}
{{{ P = 14644.18 }}}
she should invest $14,644.18 now
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(3)
{{{ A = P*( 1 + r/n )^(n*t) }}}
{{{ A = 2P }}}
{{{ r = .04 }}}
{{{ n = 4 }}}
{{{ 2P = P*( 1 + .04/4 )^(4t) }}}
{{{ 2 = ( 1 + .01 )^(4t) }}}
Take the log base 10 of both sides
{{{ log(2) = 4t*log( 1.01 ) }}}
{{{ .301 = 4t*.004321 }}}
{{{ .301 = .017285t }}}
{{{ t = 17.413 }}}
{{{ .413*12 = 4.96 }}}
it will take about 17 yrs and 5 months
to double an investment
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check answer:
{{{ 2 = ( 1 + .01 )^(4t) }}}
{{{ 2 = 1.01 ^(4*17.413) }}}
{{{ 2 = 1.01^69.652 }}}
{{{ 2 = 1.99983 }}}
close enough