# You plan on withdrawing monthly payments for the next ten years and have deposited \$100,000 inan account. If the rate of return is 8% compounded monthly, determine the value of the monthlywithdrawals.Possible answers: A) \$1,613.28 B) \$1,413.28 C) \$1,213.28 D) \$2,013.28 E) \$1,813.28

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You plan on withdrawing monthly payments for the next ten years and have deposited \$100,000 in
an account. If the rate of return is 8% compounded monthly, determine the value of the monthly
withdrawals.
Possible answers: A) \$1,613.28 B) \$1,413.28 C) \$1,213.28 D) \$2,013.28 E) \$1,813.28

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Step 1

Let's assume that the value of the monthly withdrawals be an amount A.

Interest rate = 8% per annum compounded monthly.

Hence, interest rate per period = interest rate per month = R = 8% / 12 = 0.006666667

Period = N = nos. of months in 10 years = 12 x 10 = 120 months

Present value, V = \$ 100,000

Step 2

Monthly withdrawl amount A shall be such that the sum of present value of all the future monthly withdrawal = Sum of PV of annuity A at interest rate of R and period N = A / R x [1 - (1 + R)-N] = Amount deposited in the account presently = V = \$ 100,000

Hence, we have to solve for A from the equation, A / R x [1 - (1 + R)-N]  = 100,000

Step 3

Or, A / 0.006666667 x [1 - (1 + 0.006666667)-120] = 100,000

Or, 82.42148089A = 10...

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