Question

In: Finance

You plan to withdraw $80,000 per year for 30 years after youretire at age 65....

You plan to withdraw $80,000 per year for 30 years after you retire at age 65. You are age 25 now and want to make one deposit at end of each year for 40 years then stop depositing after 40 deposits. To accumulate enough funds to afford the 30 withdrawals, you are presented with 2 options. First is an investment with 8% annual return and second one with 6% annual return. What is the difference between the annual deposit amount of the two options?

Solutions

Expert Solution

We will find the annual deposit required with an annual rate of 8% and 6%. Then take the difference between the two.

Part 1: The annual deposit required with an annual rate of 8%

First we will find the value of the retirement corpus as of age 65

PMT = 80,000

n = 30 annual payments

r = 8% per year

The value of the retirement corpus as of age 65 is $900,622.6675

Next, we will find the annual deposit required with this as the FV

FV = The value of the retirement corpus as of age 65

FV = $900,622.6675

n = 40 years

r = 8% annual rate

Annual deposit required with 8% annual return is $3,476.5489476379

Part 2: The annual deposit required with an annual rate of 6%

First, we will find the value of the retirement corpus as of age 65

PMT = 80,000

n = 30 years

r = 6% per year

The value of the retirement corpus as of age 65 is $1,101,186.4921333333

Next, we will find the annual deposit required with this as the FV

FV = The value of the retirement corpus as of age 65

FV = $1,101,186.4921333333

n = 40

r = 6%

Annual deposit required with 8% annual return is $7,115.3560743036

The difference between the annual deposit amount of the two options is (7,115.3560743036 -3,476.5489476379) = $3,638.8071266657

jeff jeffy answered 2 years ago

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