Question 1198072
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The present value of a sum of money is the amount that must be invested now, 
at a given rate of interest, to produce the desired sum at a later date.
Find the present value of $10,000 if interest is paid at a rate of 10% per year, 
compounded semiannually, for 2 years. (Round your answer up to the next cent.)
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<pre>
desired value = {{{present_value*(1 + 0.1/2)^(2*2)}}}.


{{{1+0.1/2}}} = 1.05  is the effective growth rate per half of a year.

The 2*2 in the power is 2 halves of a year taken twice, for two years.


Thus, the equation is

    10000 = {{{present_value*1.05^4}}} 

or

    10000 = {{{present_value*1.21550625}}},

which gives

    present value = {{{10000/1.21550625}}} = 8227.024748 = 8227.03 dollars, rounded up to the nearest cent.
</pre>

Solved.