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 $25,000 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 $542,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $500,000 to his nephew Frodo. He can afford to save $1,700 per month for the next 15 years.

If he can earn a 10 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?

Answer 1

Answer: Bilbo would need to save a total of $6,200 per month

Step-by-step explanation:

In order to reach his first objective of having $25,000 per month for 25 years after retirement, Bilbo would need to save $2,922 per month in Years 16 through 30. This is because he needs to accumulate enough money to cover the first withdrawal of $25,000 plus 25 years of withdrawals at the same rate, which is calculated by multiplying the amount of the first withdrawal by (1.0725/1.10)^15. To cover his second objective of purchasing a cabin in Rivendell in 15 years, he would need to save an additional $373 per month during Years 16 through 30. This is calculated by subtracting the amount he has already saved for the 15 years prior from the total cost of the cabin. Finally, to cover his third objective of leaving an inheritance of $500,000 to his nephew Frodo, he would need to save an additional $1,905 per month during Years 16 through 30. This is calculated by subtracting the amount he has already saved for the 15 years prior from the total inheritance.

Therefore, Bilbo would need to save a total of $6,200 per month in Years 16 through 30 in order to meet all three of his objectives.