Question 960779
{{{ A = P*( 1 + r/n )^( n*t ) }}}
{{{ 500 = 350*( 1 + r/1 )^( 1*3 ) }}}
{{{ 500 = 350*( 1 + r )^3 }}}
{{{ 10 = 7*( 1 + r )^3 }}}
Take the log of both sides
{{{ log( 10 ) = log( 7 ) + log( 1 + r )^3 }}}
{{{ 1 = .8451 + log( 1 + r )^3 }}}
{{{3* log( 1 + r )  = .1549 }}}
{{{ log( 1 + r ) = .05163 }}}
{{{ 1 + r = 10^.05163 }}}
{{{ 1 + r = 1.1262 }}}
{{{ r = .1262 }}}
The annual interest rate is 12.62%
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check:
{{{ 10 = 7*( 1 + r )^3 }}}
{{{ 10 = 7*( 1 + .1262 )^3 }}}
{{{ 10 = 7*1.1262^3 }}}
{{{ 10 = 7*1.42853 }}}
{{{ 10 = 9.99972 }}}
OK -error due to rounding off