Question 1201177: 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 6% per year, compounded semiannually, for 5 years. (Round your answer up to the next cent.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the amount is 10,000 and it is presumably available in 5 years.
the present value at 6% per year, compounded semi-annually is:
p = 10,000 / ((1 + .6/2) ^ (5*2))
this becomes:
p = 10,000 / (1.03 ^ 10).
solve for p (stands for present value) to get:
p = 7,440.939149.
that's how much you woud have to invest today so you can have 10,000 in 5 years.
since the annual interest rate is compounded semi-annually, then you need to find the interest rate per semi-annual period.
that is equal to .06/2 = .05
the number of time periods is 5 years * 2 semi-annual periods per year = 10 semi-annual time period.
take 7440.939149 and multiply it by 1.03 ^ 10 and you will get 10,000.
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