Suppose you plan to retire at age 70, and you want to be able towithdraw...

Suppose you plan to retire at age 70, and you want to be able to withdraw an amount of $6,000 per month beginning with the first month after your 70th birthday until you reach your birthday at age 100. If the account which contains your savings earns 7% APR compounded monthly, how much money needs to be in the account by the time you reach your 70th birthday? (Answer to the nearest dollar.)

Expert Solution

The amount is computed as shown below:

Present value = Monthly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

r is computed as follows:

= 7% / 12 (Since the payments are on monthly basis, hence divided by 12)

= 0.58333333% or 0.0058333333

n is computed as follows:

= (100 - 70) i.e. 30 year x 12 months (Since the payments are on monthly basis, hence multiplied by 12)

= 360

So, the amount is computed as follows:

= $ 6,000 x [ (1 - 1 / (1 + 0.005833333)³⁶⁰ ) / 0.005833333 ]

= $ 6,000 x 150.307574

= $ 901,845

jeff jeffy answered 2 years ago

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