Bilbo Baggins wants to save money to meet three objectives. First, he would like
ID: 2645752 • Letter: B
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 $31,000 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 10 years at an estimated cost of $410,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $1,400,000 to his nephew Frodo. He can afford to save $3,900 per month for the next 10 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 11 through 30?
I am getting annoy! I keep getting the wrong answer. I know that I am probably close. Need help.
Explanation / Answer
Answer:
Bilbo Baggins wants to earn retirement income of $31,000 per month for 25 years after his retirement. So we need to calculate the Present value of annuity at the time of retirement.
We know that Ear after retirement is 7%, hence Discount rate shall be 7% per annum
Monthly rate = 7%/12 = 0.5833% = 0.00583333
And monthly income needed is $31000
And months = 25 years *12 = 300 months
Using the Present value of annuity formula:
Present value = P *[{1-(1+r)^-n}/r]
P = Monthly income = $31000
r = 0.00583333
n = 300
Present value = 31000*[{1-(1+0.00583333)^-300}/0.00583333]
= 4386094
Hence Amount required at the end of 30 years from now (At retirement) = $4386094
Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $1,400,000 to his nephew Frodo
Hence Present value of amount at the end of 30 years from now =1400000 / (1+0.00583333)^(300) = $244524
Hence Total Amount to be in hand at the end of 30 years from now = $4386094 + $244524 = $4630618
He can invest $3900 per month today at the rate of 10% for next 10 years
F =C *[{(1+r)^(n)
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