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Question 1198672: With a present value of $140,000, what is the size of the withdrawals that can be made at the end of each quarter for the next 10 years if money is worth 7.5%, compounded quarterly? (Round your answer to the nearest cent.)
Answer by AbeAlgebraGenius(2)   (Show Source):
You can put this solution on YOUR website! For this problem, we need to use the Present Value of Ordinary Annuity formula.
W = B(r/n) / [ 1 - (1 + r/n)^-nt ].
W = Withdrawal amount every period (quarter).
B = Original balance in the account.
r = Annual interest rate.
n = Number of times interest is compounded per year
= Number of times withdrawals are made per year.
t = Number of years withdrawals are made.
In our case we have: B = 140,000 (original balance)
r = 0.075 (7.5% interest rate)
n = 4 (four quarters per year)
t = 10 (total of 10 years of withdrawals).
W = 140000 (0.075/4) / [1 - (1 + 0.075/4)^-40]
= 140000 (0.01875) / [1 - (1 + 0.01875)^-40]
= 2625 / (1 - 1.01875^-40)
= 2625 / (1 - 0.475658356)
= 2625 / 0.524341645
= 5006.28
Thus, the size of withdrawals each quarter is $5,006.28; for the next 10 years.
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