Question 978768
For now, let {{{ v }}} = the starting value of the coin
After 1 year:
Value = {{{ v + .08v }}}
After 2 years:
Value = {{{ ( v + .08v ) + ( v + .08 )*.08 }}}
Value = {{{ ( v + .08v )*( 1 + .08 ) }}}
Value = {{{ v*( 1 + .08 )^2 }}}
After 3 years:
Value = {{{ v*( 1 + .08 )^3 }}}
After 109 years:
Value = {{{ .25*( 1 + .08 )^109 }}}
Take the log of both sides
{{{ log( V ) = log(( 1.08^109 )) + log(( .25 )) }}}
{{{ log( V ) = 109*log(( 1.08 )) + log(( .25 )) }}}
{{{ log( V ) = 109*.03342 - .60206 }}}
{{{ log( V ) = 3.6432 - .60206 }}}
{{{ log( V ) = 3.04114 }}}
{{{ V =  1099.36 }}}
The coin will be worth $1,099.36 in 109 years
check:
Value = {{{ .25*( 1 + .08 )^109 }}}
Value = {{{ .25*1.08^109 }}}
Value = {{{ .25*4397.333 }}}
Value = {{{ 1099.33 }}}
OK