Question

Suppose you plan to save $8,000 per year for the 35 years you are working. In addition to the amount you are saving each year, you expect to sell your house for $600,000 in year 34 and deposit this money into your account. How much can you withdraw in equal amounts each year for the 30 years you are retired. The interest rate you will earn during the 35 years you are saving is 9%. Once you retire, you’ll reduce the amount of stock you have in your portfolio and you will now earn a return of 6% during the 30 years you are retired. Assume that you begin saving in one year and your first withdrawal is in year 36.

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Answer 1

Value of the deposit at the end of 35 yaer = Future value of annual deposit + Future value of deposit made in year 34

Future value of annual deposit =

A = Annual deposit = $8000

i= Interest rate =9% or 0.09 per annum

n =Number of year = 35 year

hence,

Future value of annual deposit =

Future value of deposit made in year 34 = $600,000 * (1+0.09)^1 = $654000

Value of the deposit at the end of 35 year = $1725686+$654000 = $2379686

the annual withdrawal after 35 yaer should be such that ots present value is equal to the value at the 35 year end = $2379686

let the annual withrawal after 35 year is ''A'' per year.

Present value of the annual withdrawal =

=> A or annual withdrawal = $172882

you can withdraw $172882 each year for the 30 years you are retired.

Note-amounts are rounded off to nearest $.