1. Bilbo Baggins wants to save money to meet three objectives. First, he would l
ID: 2734597 • Letter: 1
Question
1. 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 $24,000 per month for 25 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 25 years of withdrawals, he would like to leave an inheritance of $550,000 to his nephew Frodo. He can afford to save $2,200 per month for the next 15 years
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?
A. $9,279.79
B. $8,115.05
C. $8,920.02
D. $7,952.75
E. $8,277.35
A. $14,907.93
B. $3,965.68
C. $20,638.96
D. $15,096.75
E. $14,794.81
1. 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 $24,000 per month for 25 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 25 years of withdrawals, he would like to leave an inheritance of $550,000 to his nephew Frodo. He can afford to save $2,200 per month for the next 15 years
Explanation / Answer
Answer 1.
Present Value of Saving = 2,200*(1-(1/1.0075)^180)/0.0075 + x/(1.09^15) * (1-(1/1.0075)^180)/0.0075
= 216,905.50 + x*27.0676
Present value of His Objectives = 24,000 /1.09^30 *(1-(1/1.00583)^300)/0.00583 + 645,000/1.09^15 + 550,000/[(1.09^30)*(1.07^25)]
= 440,744.04
Present Value of Saving = Present Value of Objectives
216,905.50 + x*27.0676 = 440,744.04
X = $8,277.35
Answer 2.
Present Value = 1,900/1.08^4 * (1-(1/1.08)^26)/0.08
= $15,096.75
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