Question 954819
His investment started {{{ 5 }}} years ago
Use the formula:
{{{ A = P*( 1 + r/n )^(n*t)  }}}
{{{ P = 1500 }}}
{{{ A = 2800 }}}
{{{ t = 5 }}}
{{{ n = 4 }}}
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{{{ 2800 = 1500*( 1 + r/4 )^( 4*5) }}}
{{{ ( 1 + r/4 )^20 = 2800/1500 }}}
{{{ ( 1 + r/4 )^20 = 1.8667 }}}
Take the log of both sides
{{{ log(( ( 1 + r/4 )^20 )) = log( 1.8667 ) }}}
{{{ 20*log(( 1 + r/4 )) = log( 1.8667 ) }}}
{{{ log(( 1 + r/4 )) = (1/20)*.27107 }}}
{{{ log(( 1 + r/4 )) = .0135535 }}}
{{{ 1 + r/4 = 10^.0135535 }}}
{{{ 1 + r/4 = 1.0317 }}}
{{{ r/4 = .0317 }}}
{{{ r = .1268 }}}
The annual rate is 12.68%
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check:
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{{{ 2800 = 1500*( 1 + r/4 )^20 }}}
{{{ 2800 = 1500*( 1 + .1268/4 )^20 }}}
{{{ 2800 = 1500*( 1 + .0317 )^20 }}}
{{{ 2800 = 1500*( 1.0317 )^20 }}}
{{{ 2800 = 1500*1.86667 }}}
{{{ 2800 = 2800.0119 }}}
close enough