What lump sum of money must be deposited into a bank account at the present time so that ​$600 per month can be withdrawn for  ​give years, with the first withdrawal scheduled for six years from​ today? The interest rate is ​1/​4% per month.​ (Hint: There are  60 monthly withdrawals and they begin at the end of the month ​72   the lump of money should be $?

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
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What lump sum of money must be deposited into a bank account at the present time so that ​$600 per month can be withdrawn for  ​give years, with the first withdrawal scheduled for six years from​ today? The interest rate is ​1/​4% per month.​ (Hint: There are  60 monthly withdrawals and they begin at the end of the month ​72

 

the lump of money should be $?

Expert Solution
Introduction;

Monthly withdrawal (C) = $600

Monthly interest rate (r) = 0.0025 (i.e. 1 / 400)

Number of monthly withdrawals (n) = 60

Monthly period till 71 months (t) = 71

Value at 71 months (P71) = ?

Present value (P0) = ?

 

Present value or initial value is the discounted value of all the future cash flows to the present using appropriate discount rate.

First we will calculate value at 71 months using present value of ordinary annuity formula ant then discount it to present

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