Question 1133695
For simple interest:
{{{ I[1] = P[1]*r[1]*t }}}
{{{ I[2] = P[2]*r[2]*t }}}
{{{ I[1] + I[2] = 12000 }}}
{{{ P[1] + P[2] = 50000 }}}
{{{ r[1] = .04 }}}
{{{ r[2] = .064 }}}
{{{ t = 5 }}}
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{{{ I[1] = P[1]*.04*5 }}}
(1) {{{ I[1] = .2P[1] }}}
and
{{{ 12000 - I[1] = ( 50000 - P[1] )*.064*5 }}}
{{{ 12000 - I[1] = ( 50000 - P[1] )*.32 }}}
{{{ 12000 - I[1] = 16000 - .32P[1] }}}
(2) {{{ I[1] = .32P[1] - 4000 }}}
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Substitute (1) into (2)
{{{ .2P[1] = .32P[1] - 4000 }}}
{{{ .12P[1] = 4000 }}}
{{{ P[1] = 33333.33 }}}
{{{ P[2] = 50000 - 33333.33 }}}
{{{ P[2] = 16666.67 }}}
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$33,333.33 is invested in 4% interest account
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check:
(1) {{{ I[1] = .2*33333.33 }}}
(1) {{{ I[1] = 6666.67 }}}
and
(2) {{{ I[1] = .32P[1] - 4000 }}}
(2) {{{ 6666.67 = .32*33333.33 - 4000 }}}
(2) {{{ 6666.67 = 10666.67 - 4000 }}}
(2) {{{ 6666.67 = 6666.67 }}}
OK