Question

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Return to question Problem 4-59 Calculating Annuity Values points 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 $29,000 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 $370,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $1,250,000 to his nephew Frodo. He can afford to save $3,100 per month for the next 10 years. If he can ear 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.) $ 2775.88 0

Answer 1

Required Retirement Income per Month = $ 29000, Cabin Purchase Expense = $ 370000 at the end of Year 10, Target Inheritance = $ 1250000 at the end of 20 years post-retirement, Retirement Tenure = 20 years or 240 months

Post-Retirement EAR = 7% and Pre-Retirement = 10 %

Applicable Post-Retirement Monthly Rate = 7/12 = 0.5833 % and Applicable Pre-Retirement Monthly Rate = 10/12 = 0.8333 %

If current time is assumed to be t=0, then Value of Retirement Income at the end of Year 30 = 29000 x (1/0.005833) x [1-{1/(1.005833)^(240)}] = $ 3740608.53

Value of Cabin Purchase Expense at the end of Year 30 = 370000 x (1.1)^(20) = $ 2489174.98

Value of Inheritance at the end of Year 30 = 1250000 / (1.07)^(20) = $ 323023.75

Total Expense Value at the end of Year 30 = 3740608.53 + 2489174.98 + 323023.75 = $ 6552807.265

Deposits between Year 1 and Year 10 Per Month = $ 3100

Value of Initial Deposits at the end of Year 30 = [3100 x (1.008333)^(119) + .............+ 3100] x (1.1)^(20) = $ 4271995.35

Let the required monthly deposits be $ k

Value of Deposits between Year 11 and Year 30 at the end of Year 30 = k x (1.008333)^(239) + .............+ k = [{(1.008333)^(240)-1}/{(1.008333)-1}] x k = k x 759.329

k x 759.329 + 4271995.35 = 6552807.265

k = (6552807.265 - 4271995.35) / 759.329 = $ 3003.718 ~ $ 3003.72