Question 1067717
Use the formula {{{ I = P*r*t }}}
where {{{ t = 1 }}} yr
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For interest on the CD:
{{{ I[1] = P[1]*r[1]*t }}}
{{{ I[1] = P[1]*.04*1 }}}
(1) {{{ I[1] = .04P[1] }}}
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For interest on the savings bond:
{{{ I[2] = P[2]*r[2]*t }}}
{{{ I[2] = ( 9000 - P[1] )*.07*1 }}}
{{{ I[2] = .07*9000 - .07*P[1] }}}
(2) {{{ I[2] = 630 - .07P[1] }}}
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(3) {{{ I[1] + I[2] = 540 }}}
(3) {{{ I[2] = 540 - I[1] }}}
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Plug (1) into (3)
(3) {{{ I[2] = 540 - .04P[1] }}}
Plug (3) into (2)
(2) {{{ 540 - .04P[1] = 630 - .07P[1] }}}
(2) {{{ .03P[1] = 90 }}}
(2) {{{ P[1] = 3000 }}}
and
(1) {{{ I[1] = .04P[1] }}}
(1) {{{ I[1] = .04*3000 }}}
(1) {{{ I[1] = 120 }}}
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$3,000 was invested in the CD account
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check:
{{{ P[1] + P[2] = 9000 }}}
{{{ P[2] = 9000 - 3000 }}}
{{{ P[2] = 6000 }}}
and
{{{ I[2] = 540 - I[1] }}}
{{{ I[2] = 540 - 120 }}}
{{{ I[2] = 420 }}}
and
{{{ I[2] = P[2]*r[2]*t }}}
{{{ 420 = 6000*.07 }}}
{{{ 420 = 420 }}}
OK