.
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.)
~~~~~~~~~~~~~~~~~~~
desired value = .
= 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 =
or
10000 = ,
which gives
present value = = 8227.024748 = 8227.03 dollars, rounded up to the nearest cent.
Solved.