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 $

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.

RELATED QUESTIONS
The present value of a sum of money is the amount that must be invested now, at a given... (answered by ikleyn)

How do I salve this type of question: The present value of a sum of money is the amount (answered by ankor@dixie-net.com)

suppose 20,000 is invested at 5 % . How much additional money must be invested at 4 % to... (answered by jim_thompson5910)

If an amount of $9,000 is invested at a simple interest rate of 3 1/2% interest per (answered by ikleyn,greenestamps)

Given that the amount in an account earning continuous interest is given by the formula... (answered by lwsshak3)

1st question: The principal P is borrowed at a simple interest rate r for a period of (answered by ikleyn)

A family invested $10,000 at 8% annual interest. How much additional money must be... (answered by mananth)

the future value of a simple interest investment is given by S = P(1+rt). What principal (answered by solver91311)

The future value of a simple interest investment is given by S=P(1+rt). What principal P... (answered by tommyt3rd)