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

Suppose you plan to retire at age 70, and you want to be able to withdraw an amount of $80,000 per year on each birthday from age 70 to age 100 (a total of 31 withdrawals). If the account which contains your savings earns 6% per year simple interest, how much money needs to be in the account by the time you reach your 70th birthday? (Answer to the nearest dollar.)

Hint: This can be solved as a 30-year ordinary annuity plus one withdrawal at age 70, or as a 31-year annuity due.

Solutions

Expert Solution

ANSWER : $ 1,181,186 (rounded to the nearest dollar)

i.e. $ 1,181,186 needs to be in the account by the time you reach your 70th birthday

Working Notes:

To calculate the amount that needs to be in the account by the time you reach your 70th birthday, we need to calculate the Present Value of all the withdrawals.

Calculation of Present Value of annuity ( Annuity due) :

Annuity Due is when the cash Flows arises at the beginning of each year.

As per the facts of Question, Present Value of annuity due can be calculated as below:

We Know that,

or it can be written as,

[where,

PV = Present Value of Annuity Due

CF = Cash Flows = $ 80,000

PVAF = Present Value annuity factor

R = Interest rate = 6%

n = Number of Periods= 31]

(using calculator)

Therefore, PV = 1181186.49193 or = $ 1181186.49

jeff jeffy answered 1 year ago

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