SOLUTION: You just sold a house for $200,000. You can invest the money at 5%/a compounded semiannually. How much could you withdraw every 6 months, starting in 6 months, for the next 20 year

Question 1185416: You just sold a house for $200,000. You can invest the money at 5%/a compounded semiannually. How much could you withdraw every 6 months, starting in 6 months, for the next 20 years?

Answer by ikleyn(52874) (Show Source): You can put this solution on YOUR website!
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You just sold a house for $200,000. You can invest the money at 5%/a compounded semiannually.
How much could you withdraw every 6 months, starting in 6 months, for the next 20 years?
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This problem is about a sinking fund.
The starting amount is A = $200,000.
The fund is compounded semi-annually at the annual compounding rate r = 5%.
You want to withdraw a regular amount at the end of each 6 months period during next 20 years.
They want you determine the value of this regular withdraw amount W.


Use the formula for a sinking fund


    A = ,    (1)


where A is the starting amount, W is the regular withdraw amount semi-annually, 
r is the annual compounding rate, m is the number of withdrawals per year (m= 2 in this problem), 
n is the total number of withdrawals/compounding (twice the number of years, in this problem),
  is the effective rate of compounding per the 6 months period.


With the given data, formula (1) takes the form


    200000 =  =  = W*25.102775  dollars.


From this equation, we find the semiannual withdraw value

    W  =  = 7967.25 dollars. 


ANSWER.  The semi-annual withdrawal value is  $7967.25.

Solved.

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