Question 960657
One million = {{{ 10^6 }}}
The formula for compound interest is:
{{{ A = P*( 1 + r/n )^(n*t) }}}
Principle is compounded quarterly, so
{{{ n = 4 }}}
{{{ A = 10^6 }}}
{{{ t = 64 }}}
{{{ r = .13 }}}
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{{{ A = P*( 1 + r/n )^(n*t) }}}
{{{ 10^6 = P*( 1 + .13/4 )^( 4*64 ) }}}
{{{ 10^6 = P*1.0325^256  }}}
{{{ 10^6 = P*3596.2961 }}}
{{{ P = 10^6 / 3596.2961 }}}
{{{ P = 278.06 }}}
You need to invest $278.06 today
check:
{{{ 10^6 = P*( 1 + .13/4 )^( 4*64 ) }}}
{{{ 10^6 = 278.06*( 1 + .13/4 )^( 4*64 ) }}}
{{{ 10^6 = 278.06*1.0325^256 }}}
Take the log of both sides
{{{ 6 = log( 278.06 ) + 256*log( 1.0325 ) }}}
{{{ 6 = 2.4441 + 256*.01389 }}}
{{{ 6 = 2.4441 + 3.5559 }}}
{{{ 6 = 6 }}}
OK