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 retirement income of $28,000 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 15 years at an estimated cost of $645,000. 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 $2,200 per month for the next 15 years.

  

Required:

If he can earn a 9 percent EAR before he retires and a 7 percent EAR after he retires, how much will he have to save each month in years 16 through 30?

rev: 09_17_2012

$9,154.25

$8,795.26

$9,798.50

$10,139.49

$8,974.75

Answer 1

Solution :-

In case EAR = 7%

One month Rate = ( 1 + 0.07 )^1/12 - 1 = 0.00565 = 0.5654%

In case EAR = 9%

One month Rate = ( 1 + 0.09 )^1/12 - 1 = 0.007207 = 0.7207%

Amount Needed after retirement = Amount for inheritance and Amount of Annuity after retirement

Present Value of amount of inheritance at the time of Retirement = $800,000 / ( 1 + 0.07 )²⁰

= $800,000 * 0.2584 = $206,735.20

Present value of 20 years ( 240 months ) monthly annuity at the time of Retirement = $28,000 * PVAF ( 0.5654% , 240 )

= $28,000 * 113.1588

= $3,672,447.27

Now the Value at Retirement of the Amount Required After Retirement = $206,735.20 + $3,672,447.27

= $3,879,182.47

Now the Future Value of Monthly Saving after 15 Years ( 15 * 12 ) = 180 months = $2,200 * FVAF ( 0.7207% , 180 )

= $2,200 * 366.626

= $806,576.72

Cost of Cabin = $645,000

Net Value of Saving at the end of 15 Years = $806,576.72 - $645,000 = $161,576.72

Now the Value of $161,576.72 at the time of Retirement =$161,576.72 * ( 1 + 0.09 )¹⁵ = $588,504.40

Now Future More amount Required = $3,879,182.47 - $588,504.40 = $3,290,642.10

Let amount of Monthly Deposit for 15 Years be X

Now X * FVAF ( 0.7207% , 180 ) = $3,290,642.10

X * 366.626 = $3,290,642.10

X = $8,974.75

Therefore Correct Answer is (E)

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