Question

Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with a retirement income of $33,000 per month for 20 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $410,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $800,000 to his nephew Frodo. He can afford to save $3,900 per month for the next 10 years. If he can earn an EAR of 10 percent before he retires and an EAR of 7 percent after he retires, how much will he have to save each month in Years 11 through 30? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

need help finding answer on the financial calculator

Monthly savings ??

$

Answer 1

He deposit $3,500 per month for next 10 year.

So future value of monthly deposit at interest rate of 10% is calculated in excel and screen shot provided below:

Future value of monthly deposits is $798,895.42 out of which he purchase cabin in Rivendell for $410,000.

So total value of saving remains = $798,895.42 - $410,000

                                                    = $388,895.42.

Total value remains as saving after 10 year is $388,895.42.

Now

He wants to withdraw $33,000 per month for 20 year and $800,000 remains for his nephew after 20 year.

Value of Inheritance at time of retirement = $800,000 / (1 + 7%) ^ 20

= $800,000 / 3.8697

= $206,735.20.

Value of Inheritance at time of retirement is $206,735.20.

So present value of monthly withdrawal time of retirement at discount rate of 7% is calculated in excel and screen shot provided below:

present value of monthly withdrawal time of retirement is $4,281,251.85.

Total amount required at time of retirement = $4,281,251.85 + $206,735.20.

= $4,487,987.05.

Total amount required at time of retirement is $4,487,987.05.

Value of saving after 10 year = $388,895.42

Value of saving at time of retirement = $388,895.42 × (1 + 10%) ^ 20

=  $388,895.42 × 6.7275

= $2,616,293.90.

Value of saving at time of retirement will be $2,616,293.90.

Total amount required through monthly saving = $4,487,987.05 - $2,616,293.90

= $1,871,693.15

Total amount required through monthly saving is $1,871,693.15.

Total monthly saving from year 11 to 30 is calculated in excel and screen shot provided below:

Total monthly saving from year 11 to 30 is $2,464.80.