SOLUTION: 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 $

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Question 1198072: 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.)

Answer by ikleyn(52786) About Me  (Show Source):
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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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desired value = present_value%2A%281+%2B+0.1%2F2%29%5E%282%2A2%29.


1%2B0.1%2F2 = 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%2A1.05%5E4 

or

    10000 = present_value%2A1.21550625,

which gives

    present value = 10000%2F1.21550625 = 8227.024748 = 8227.03 dollars, rounded up to the nearest cent.

Solved.